The many-body localization transition in quasiperiodic systems has been extensively studied in recent ultracold atom experiments. At intermediate quasiperiodic potential strength, a surprising Griffiths-like regime with slow dynamics appears in the absence of random disorder and mobility edges. In this work, we study the interacting Aubry-Andre model, a prototype quasiperiodic system, as a function of incommensurate potential strength using a novel dynamical measure, information scrambling, in a large system of 200 lattice sites. Between the thermal phase and the many-body localized phase, we find an intermediate dynamical phase where the butterfly velocity is zero and information spreads in space as a power-law in time. This is in contrast to the ballistic spreading in the thermal phase and logarithmic spreading in the localized phase. We further investigate the entanglement structure of the many-body eigenstates in the intermediate phase and find strong fluctuations in eigenstate entanglement entropy within a given energy window, which is inconsistent with the eigenstate thermalization hypothesis. Machine-learning on the entanglement spectrum also reaches the same conclusion. Our large-scale simulations suggest that the intermediate phase with vanishing butterfly velocity could be responsible for the slow dynamics seen in recent experiments.

%8 02/19/2019 %G eng %U https://arxiv.org/abs/1902.07199 %0 Journal Article %D 2019 %T Chaos in a quantum rotor model %A Gong Cheng %A Brian Swingle %XWe study scrambling in a model consisting of a number N of M-component quantum rotors coupled by random infinite-range interactions. This model is known to have both a paramagnetic phase and a spin glass phase separated by second order phase transition. We calculate in perturbation theory the squared commutator of rotor fields at different sites in the paramagnetic phase, to leading non-trivial order at large N and large M. This quantity diagnoses the onset of quantum chaos in this system, and we show that the squared commutator grows exponentially with time, with a Lyapunov exponent proportional to 1M. At high temperature, the Lyapunov exponent limits to a value set by the microscopic couplings, while at low temperature, the exponent exhibits a T4 dependence on temperature T.

%8 01/29/2019 %G eng %U https://arxiv.org/abs/1901.10446 %0 Journal Article %D 2019 %T A characterization of quantum chaos by two-point correlation functions %A Hrant Gharibyan %A Masanori Hanada %A Brian Swingle %A Masaki Tezuka %XWe propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).

%8 02/28/2019 %G eng %U https://arxiv.org/abs/1902.11086 %0 Journal Article %D 2019 %T Circuit Complexity across a Topological Phase Transition %A Fangli Liu %A Rex Lundgren %A Paraj Titum %A James R. Garrison %A Alexey V. Gorshkov %XWe use Nielsen's approach to quantify the circuit complexity in the one-dimensional Kitaev model. In equilibrium, we find that the circuit complexity of ground states exhibits a divergent derivative at the critical point, signaling the presence of a topological phase transition. Out of equilibrium, we study the complexity dynamics after a sudden quench, and find that the steady-state complexity exhibits nonanalytical behavior when quenched across critical points. We generalize our results to the long-range interacting case, and demonstrate that the circuit complexity correctly predicts the critical point between regions with different semi-integer topological numbers. Our results establish a connection between circuit complexity and quantum phase transitions both in and out of equilibrium, and can be easily generalized to topological phase transitions in higher dimensions. Our study opens a new avenue to using circuit complexity as a novel quantity to understand many-body systems.

%8 03/27/2019 %G eng %U https://arxiv.org/abs/1902.10720 %0 Journal Article %J Proceedings of TQC 2019, LIPIcs %D 2019 %T Circuit Transformations for Quantum Architectures %A Andrew M. Childs %A Eddie Schoute %A Cem M. Unsal %XQuantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits to architecture qubits. To achieve this, we first consider the qubit movement subproblem and use the routing via matchings framework to prove tighter bounds on parallel routing. In practice, we only need to perform partial permutations, so we generalize routing via matchings to that setting. We give new routing procedures for common architecture graphs and for the generalized hierarchical product of graphs, which produces subgraphs of the Cartesian product. Secondly, for serial routing, we consider the token swapping framework and extend a 4-approximation algorithm for general graphs to support partial permutations. We apply these routing procedures to give several circuit transformations, using various heuristic qubit placement subroutines. We implement these transformations in software and compare their performance for large quantum circuits on grid and modular architectures, identifying strategies that work well in practice.

%B Proceedings of TQC 2019, LIPIcs %V 135 %8 02/25/2019 %G eng %U https://arxiv.org/abs/1902.09102 %N 3 %& 1-3:24 %R https://doi.org/10.4230/LIPIcs.TQC.2019.3 %0 Journal Article %D 2019 %T Competing (Semi)-Selfish Miners in Bitcoin %A Francisco J. Marmolejo-Cossío %A Eric Brigham %A Benjamin Sela %A Jonathan Katz %XThe Bitcoin protocol prescribes certain behavior by the miners who are responsible for maintaining and extending the underlying blockchain; in particular, miners who successfully solve a puzzle, and hence can extend the chain by a block, are supposed to release that block immediately. Eyal and Sirer showed, however, that a selfish miner is incentivized to deviate from the protocol and withhold its blocks under certain conditions. The analysis by Eyal and Sirer, as well as in followup work, considers a \emph{single} deviating miner (who may control a large fraction of the hashing power in the network) interacting with a remaining pool of honest miners. Here, we extend this analysis to the case where there are \emph{multiple} (non-colluding) selfish miners. We find that with multiple strategic miners, specific deviations from honest mining by multiple strategic agents can outperform honest mining, even if individually miners would not be incentivised to be dishonest. This previous point effectively renders the Bitcoin protocol to be less secure than previously thought.

%8 06/11/2019 %G eng %U https://arxiv.org/abs/1906.04502 %0 Journal Article %D 2019 %T Complexity phase diagram for interacting and long-range bosonic Hamiltonians %A Nishad Maskara %A Abhinav Deshpande %A Minh C. Tran %A Adam Ehrenberg %A Bill Fefferman %A Alexey V. Gorshkov %XRecent years have witnessed a growing interest in topics at the intersection of many-body physics and complexity theory. Many-body physics aims to understand and classify emergent behavior of systems with a large number of particles, while complexity theory aims to classify computational problems based on how the time required to solve the problem scales as the problem size becomes large. In this work, we use insights from complexity theory to classify phases in interacting many-body systems. Specifically, we demonstrate a "complexity phase diagram" for the Bose-Hubbard model with long-range hopping. This shows how the complexity of simulating time evolution varies according to various parameters appearing in the problem, such as the evolution time, the particle density, and the degree of locality. We find that classification of complexity phases is closely related to upper bounds on the spread of quantum correlations, and protocols to transfer quantum information in a controlled manner. Our work motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.

%8 06/10/2019 %G eng %U https://arxiv.org/abs/1906.04178 %0 Journal Article %J Phys. Rev. Lett. %D 2019 %T Confined Dynamics in Long-Range Interacting Quantum Spin Chains %A Fangli Liu %A Rex Lundgren %A Paraj Titum %A Guido Pagano %A Jiehang Zhang %A Christopher Monroe %A Alexey V. Gorshkov %XWe study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law (1/rα) interactions. We find that long-range interactions give rise to a confining potential, which couples pairs of domain walls (kinks) into bound quasiparticles, analogous to mesonic bound states in high-energy physics. We show that these bound states have dramatic consequences for the non-equilibrium dynamics following a global quantum quench, such as suppressed spreading of quantum information and oscillations of order parameters. The masses of these bound states can be read out from the Fourier spectrum of these oscillating order parameters. We then use a two-kink model to qualitatively explain the phenomenon of long-range-interaction-induced confinement. The masses of the bound states predicted by this model are in good quantitative agreement with exact diagonalization results. Moreover, we illustrate that these bound states lead to weak thermalization of local observables for initial states with energy near the bottom of the many-body energy spectrum. Our work is readily applicable to current trapped-ion experiments.

%B Phys. Rev. Lett. %V 122 %8 04/17/2019 %G eng %U https://arxiv.org/abs/1810.02365 %N 150601 %R https://doi.org/10.1103/PhysRevLett.122.150601 %0 Journal Article %D 2019 %T Discrete Time Crystals %A Dominic V. Else %A Christopher Monroe %A Chetan Nayak %A Norman Y. Yao %XExperimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new non-equilibrium phases of matter. In particular, we focus on "discrete time crystals", which are many-body phases of matter characterized by a spontaneously broken discrete time translation symmetry. We give a definition of discrete time crystals from several points of view, emphasizing that they are a non-equilibrium phenomenon, which is stabilized by many-body interactions, with no analog in non-interacting systems. We explain the theory behind several proposed models of discrete time crystals, and compare a number of recent realizations, in different experimental contexts.

%8 05/30/2019 %G eng %U https://arxiv.org/abs/1905.13232 %0 Journal Article %D 2019 %T Distributional property testing in a quantum world %A Andras Gilyen %A Tongyang Li %XA fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing closeness between unknown distributions, testing independence between two distributions, and estimating the Shannon / von Neumann entropy of distributions. The distributions can be either classical or quantum, however our quantum algorithms require coherent quantum access to a process preparing the samples. Our results build on the recent technique of quantum singular value transformation, combined with more standard tricks such as divide-and-conquer. The presented approach is a natural fit for distributional property testing both in the classical and the quantum case, demonstrating the first speed-ups for testing properties of density operators that can be accessed coherently rather than only via sampling; for classical distributions our algorithms significantly improve the precision dependence of some earlier results.

%8 02/02/2019 %G eng %U https://arxiv.org/abs/1902.00814 %0 Journal Article %D 2019 %T Equilibration to the non-Abelian thermal state in quantum many-body physics %A Nicole Yunger Halpern %A Michael E. Beverland %A Amir Kalev %XIn statistical mechanics, a small system exchanges conserved charges---heat, particles, electric charge, etc.---with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the charges. The charges are usually represented by operators assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed "the non-Abelian thermal state (NATS)." We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which form the system of interest. The conserved charges manifest as spin components. Heisenberg interactions push the charges between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting charges from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.

%8 6/21/2019 %G eng %U https://arxiv.org/abs/1906.09227 %0 Journal Article %D 2019 %T Floquet engineering of optical lattices with spatial features and periodicity below the diffraction limit %A S. Subhankar %A P. Bienias %A P. Titum %A T-C. Tsui %A Y. Wang %A A. V. Gorshkov %A S. L. Rolston %A J. V. Porto %XFloquet engineering or coherent time periodic driving of quantum systems has been successfully used to synthesize Hamiltonians with novel properties. In ultracold atomic systems, this has led to experimental realizations of artificial gauge fields, topological band structures, and observation of dynamical localization, to name just a few. Here we present a Floquet-based framework to stroboscopically engineer Hamiltonians with spatial features and periodicity below the diffraction limit of light used to create them by time-averaging over various configurations of a 1D optical Kronig-Penney (KP) lattice. The KP potential is a lattice of narrow subwavelength barriers spaced by half the optical wavelength (λ/2) and arises from the non-linear optical response of the atomic dark state. Stroboscopic control over the strength and position of this lattice requires time-dependent adiabatic manipulation of the dark state spin composition. We investigate adiabaticity requirements and shape our time-dependent light fields to respect the requirements. We apply this framework to show that a λ/4-spaced lattice can be synthesized using realistic experimental parameters as an example, discuss mechanisms that limit lifetimes in these lattices, explore candidate systems and their limitations, and treat adiabatic loading into the ground band of these lattices.

%8 06/18/2019 %G eng %U https://arxiv.org/abs/1906.07646 %0 Journal Article %J Phys. Rev. Lett. (in press) %D 2019 %T Fluctuation-induced torque on a topological insulator out of thermal equilibrium %A M. F. Maghrebi %A Alexey V. Gorshkov %A J. D. Sau %XTopological insulators with the time reversal symmetry broken exhibit strong magnetoelectric and magneto-optic effects. While these effects are well-understood in or near equilibrium, nonequilibrium physics is richer yet less explored. We consider a topological insulator thin film, weakly coupled to a ferromagnet, out of thermal equilibrium with a cold environment (quantum electrodynamics vacuum). We show that the heat flow to the environment is strongly circularly polarized, thus carrying away angular momentum and exerting a purely fluctuation-driven torque on the topological insulator film. Utilizing the Keldysh framework, we investigate the universal nonequilibrium response of the TI to the temperature difference with the environment. Finally, we argue that experimental observation of this effect is within reach.

%B Phys. Rev. Lett. (in press) %G eng %U https://arxiv.org/abs/1811.06080 %0 Journal Article %J Quantum %D 2019 %T Graphical Methods in Device-Independent Quantum Cryptography %A Spencer Breiner %A Carl Miller %A Neil J. Ross %XWe introduce a framework for graphical security proofs in device-independent quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography more accessible, facilitate the discovery of new proofs, and enable automated proof verification. As an example of our framework, we reprove a recent result from device-independent quantum cryptography: any linear randomness expansion protocol can be converted into an unbounded randomness expansion protocol. We give a graphical exposition of a proof of this result and implement parts of it in the Globular proof assistant.

%B Quantum %V 3 %8 05/20/2019 %G eng %U https://arxiv.org/abs/1705.09213 %N 146 %R https://doi.org/10.22331/q-2019-05-27-146 %0 Journal Article %D 2019 %T Gravitational Direct Detection of Dark Matter %A Daniel Carney %A Sohitri Ghosh %A Gordan Krnjaic %A Jacob M. Taylor %XThe only coupling dark matter is guaranteed to have with the standard model is through gravity. Here we propose a concept for direct dark matter detection using only this gravitational coupling, enabling a new regime of detection. Leveraging dramatic advances in the ability to create, maintain, and probe quantum states of massive objects, we suggest that an array of quantum-limited impulse sensors may be capable of detecting the correlated gravitational force created by a passing dark matter particle. We present two concrete realizations of this scheme, using either mechanical resonators or freely-falling masses. With currently available technology, a meter-scale apparatus of this type could detect any dark matter candidate around the Planck mass or heavier.

%8 03/01/2019 %G eng %U https://arxiv.org/abs/1903.00492 %0 Journal Article %D 2019 %T Ground-state energy estimation of the water molecule on a trapped ion quantum computer %A Yunseong Nam %A Jwo-Sy Chen %A Neal C. Pisenti %A Kenneth Wright %A Conor Delaney %A Dmitri Maslov %A Kenneth R. Brown %A Stewart Allen %A Jason M. Amini %A Joel Apisdorf %A Kristin M. Beck %A Aleksey Blinov %A Vandiver Chaplin %A Mika Chmielewski %A Coleman Collins %A Shantanu Debnath %A Andrew M. Ducore %A Kai M. Hudek %A Matthew Keesan %A Sarah M. Kreikemeier %A Jonathan Mizrahi %A Phil Solomon %A Mike Williams %A Jaime David Wong-Campos %A Christopher Monroe %A Jungsang Kim %XQuantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly-interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here, we describe a scalable co-design framework for solving chemistry problems on a trapped ion quantum computer, and apply it to compute the ground-state energy of the water molecule. The robust operation of the trapped ion quantum computer yields energy estimates with errors approaching the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics.

%8 03/07/2019 %G eng %U https://arxiv.org/abs/1902.10171 %0 Journal Article %D 2019 %T Heisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks %A Kevin Qian %A Zachary Eldredge %A Wenchao Ge %A Guido Pagano %A Christopher Monroe %A James V. Porto %A Alexey V. Gorshkov %XWe generalize past work on quantum sensor networks to show that, for d input parameters, entanglement can yield a factor O(d) improvement in mean squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.

%8 01/25/2019 %G eng %U https://arxiv.org/abs/1901.09042 %0 Journal Article %D 2019 %T How Low Can Vacuum Energy Go When Your Fields Are Finite-Dimensional? %A ChunJun Cao %A Aidan Chatwin-Davies %A Ashmeet Singh %XAccording to the holographic bound, there is only a finite density of degrees of freedom in space when gravity is taken into account. Conventional quantum field theory does not conform to this bound, since in this framework, infinitely many degrees of freedom may be localized to any given region of space. In this essay, we explore the viewpoint that quantum field theory may emerge from an underlying theory that is locally finite-dimensional, and we construct a locally finite-dimensional version of a Klein-Gordon scalar field using generalized Clifford algebras. Demanding that the finite-dimensional field operators obey a suitable version of the canonical commutation relations makes this construction essentially unique. We then find that enforcing local finite dimensionality in a holographically consistent way leads to a huge suppression of the quantum contribution to vacuum energy, to the point that the theoretical prediction becomes plausibly consistent with observations.

%8 05/11/2019 %G eng %U https://arxiv.org/abs/1905.11199 %0 Journal Article %J Phys. Rev. %D 2019 %T Interacting Qubit-Photon Bound States with Superconducting Circuits %A Neereja M. Sundaresan %A Rex Lundgren %A Guanyu Zhu %A Alexey V. Gorshkov %A Andrew A. Houck %XQubits strongly coupled to a photonic crystal give rise to many exotic physical scenarios, beginning with single and multi-excitation qubit-photon dressed bound states comprising induced spatially localized photonic modes, centered around the qubits, and the qubits themselves. The localization of these states changes with qubit detuning from the band-edge, offering an avenue of in situ control of bound state interaction. Here, we present experimental results from a device with two qubits coupled to a superconducting microwave photonic crystal and realize tunable on-site and inter-bound state interactions. We observe a fourth-order two photon virtual process between bound states indicating strong coupling between the photonic crystal and qubits. Due to their localization-dependent interaction, these states offer the ability to create one-dimensional chains of bound states with tunable and potentially long-range interactions that preserve the qubits' spatial organization, a key criterion for realization of certain quantum many-body models. The widely tunable, strong and robust interactions demonstrated with this system are promising benchmarks towards realizing larger, more complex systems of bound states.

%B Phys. Rev. %V X 9 %8 2018/01/30 %G eng %U http://arxiv.org/abs/1801.10167 %N 011021 %R https://doi.org/10.1103/PhysRevX.9.011021 %0 Journal Article %J Ann. Phys. %D 2019 %T Interaction-induced transition in the quantum chaotic dynamics of a disordered metal %A S. V. Syzranov %A Alexey V. Gorshkov %A V. M. Galitski %XWe demonstrate that a weakly disordered metal with short-range interactions exhibits a transition in the quantum chaotic dynamics when changing the temperature or the interaction strength. For weak interactions, the system displays exponential growth of the out-of-time-ordered correlator (OTOC) of the current operator. The Lyapunov exponent of this growth is temperature-independent in the limit of vanishing interaction. With increasing the temperature or the interaction strength, the system undergoes a transition to a non-chaotic behaviour, for which the exponential growth of the OTOC is absent. We conjecture that the transition manifests itself in the quasiparticle energy-level statistics and also discuss ways of its explicit observation in cold-atom setups.

%B Ann. Phys. %V 405 %8 03/25/2019 %G eng %U https://arxiv.org/abs/1709.09296 %N 1 %R https://doi.org/10.1016/j.aop.2019.03.008 %0 Journal Article %D 2019 %T Interpreting Neural Networks Using Flip Points %A Roozbeh Yousefzadeh %A Dianne P. O'Leary %XNeural networks have been criticized for their lack of easy interpretation, which undermines confidence in their use for important applications. Here, we introduce a novel technique, interpreting a trained neural network by investigating its flip points. A flip point is any point that lies on the boundary between two output classes: e.g. for a neural network with a binary yes/no output, a flip point is any input that generates equal scores for "yes" and "no". The flip point closest to a given input is of particular importance, and this point is the solution to a well-posed optimization problem. This paper gives an overview of the uses of flip points and how they are computed. Through results on standard datasets, we demonstrate how flip points can be used to provide detailed interpretation of the output produced by a neural network. Moreover, for a given input, flip points enable us to measure confidence in the correctness of outputs much more effectively than softmax score. They also identify influential features of the inputs, identify bias, and find changes in the input that change the output of the model. We show that distance between an input and the closest flip point identifies the most influential points in the training data. Using principal component analysis (PCA) and rank-revealing QR factorization (RR-QR), the set of directions from each training input to its closest flip point provides explanations of how a trained neural network processes an entire dataset: what features are most important for classification into a given class, which features are most responsible for particular misclassifications, how an adversary might fool the network, etc. Although we investigate flip points for neural networks, their usefulness is actually model-agnostic.

%8 03/20/2019 %G eng %U https://arxiv.org/abs/1903.08789 %0 Journal Article %J Commun. Math. Phys. %D 2019 %T Limitations of semidefinite programs for separable states and entangled games %A Aram W. Harrow %A Anand Natarajan %A Xiaodi Wu %XSemidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These are based on new limitations on the sum-of-squares (SoS) hierarchy in approximating two particularly important sets in quantum information theory, where previously no ω(1)-round integrality gaps were known: the set of separable (i.e. unentangled) states, or equivalently, the 2→4 norm of a matrix, and the set of quantum correlations; i.e. conditional probability distributions achievable with local measurements on a shared entangled state. In both cases no-go theorems were previously known based on computational assumptions such as the Exponential Time Hypothesis (ETH) which asserts that 3-SAT requires exponential time to solve. Our unconditional results achieve the same parameters as all of these previous results (for separable states) or as some of the previous results (for quantum correlations). In some cases we can make use of the framework of Lee-Raghavendra-Steurer (LRS) to establish integrality gaps for any SDP, not only the SoS hierarchy. Our hardness result on separable states also yields a dimension lower bound of approximate disentanglers, answering a question of Watrous and Aaronson et al. These results can be viewed as limitations on the monogamy principle, the PPT test, the ability of Tsirelson-type bounds to restrict quantum correlations, as well as the SDP hierarchies of Doherty-Parrilo-Spedalieri, Navascues-Pironio-Acin and Berta-Fawzi-Scholz.

%B Commun. Math. Phys. %V 366 %8 03/04/2019 %G eng %U https://arxiv.org/abs/1612.09306 %N 2 %& 423-468 %R https://doi.org/10.1007/s00220-019-03382-y %0 Journal Article %J Phys. Rev. X 9, 031006 %D 2019 %T Locality and digital quantum simulation of power-law interactions %A Minh Cong Tran %A Andrew Y. Guo %A Yuan Su %A James R. Garrison %A Zachary Eldredge %A Michael Foss-Feig %A Andrew M. Childs %A Alexey V. Gorshkov %XThe propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/rα. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al. [arXiv:1801.03922]. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α>3D (where D is the number of dimensions).

%B Phys. Rev. X 9, 031006 %V 9 %8 07/10/2019 %G eng %U https://arxiv.org/abs/1808.05225 %N 031006 %R https://doi.org/10.1103/PhysRevX.9.031006 %0 Journal Article %J Physical Review Letters %D 2019 %T Nearly optimal lattice simulation by product formulas %A Andrew M. Childs %A Yuan Su %XProduct formulas provide a straightforward yet surprisingly efficient approach to quantum simulation. We show that this algorithm can simulate an n-qubit Hamiltonian with nearest-neighbor interactions evolving for time t using only (nt)1+o(1) gates. While it is reasonable to expect this complexity---in particular, this was claimed without rigorous justification by Jordan, Lee, and Preskill---we are not aware of a straightforward proof. Our approach is based on an analysis of the local error structure of product formulas, as introduced by Descombes and Thalhammer and significantly simplified here. We prove error bounds for canonical product formulas, which include well-known constructions such as the Lie-Trotter-Suzuki formulas. We also develop a local error representation for time-dependent Hamiltonian simulation, and we discuss generalizations to periodic boundary conditions, constant-range interactions, and higher dimensions. Combined with a previous lower bound, our result implies that product formulas can simulate lattice Hamiltonians with nearly optimal gate complexity.

%B Physical Review Letters %G eng %U https://arxiv.org/abs/1901.00564 %0 Journal Article %D 2019 %T Non-equilibrium fixed points of coupled Ising models %A Jeremy T. Young %A Alexey V. Gorshkov %A Michael Foss-Feig %A Mohammad F. Maghrebi %XDriven-dissipative systems can exhibit non-equilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions present in these systems generically exhibit an effectively classical equilibrium behavior in spite of their quantum non-equilibrium origin. In this paper, we show that multicritical points in driven-dissipative systems can give rise to genuinely non-equilibrium behavior. We investigate a non-equilibrium driven-dissipative model of interacting bosons that exhibits two distinct phase transitions: one from a high- to a low-density phase---reminiscent of a liquid-gas transition---and another to an antiferromagnetic phase. Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) Z2 symmetry. They, however, coalesce at a multicritical point giving rise to a non-equilibrium model of coupled Ising-like order parameters described by a Z2×Z2 symmetry. Using a dynamical renormalization-group approach, we show that a pair of non-equilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system. We elucidate various exotic features of these NEFPs. In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance. This further results in complex-valued critical exponents, spiraling phase boundaries, and a complex Liouvillian gap even close to the phase transition. As direct evidence of the non-equilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths. Finally, we argue that this non-equilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.

%8 03/06/2019 %G eng %U https://arxiv.org/abs/1903.02569 %0 Journal Article %D 2019 %T Opportunities for Nuclear Physics & Quantum Information Science %A I. C. Cloët %A Matthew R. Dietrich %A John Arrington %A Alexei Bazavov %A Michael Bishof %A Adam Freese %A Alexey V. Gorshkov %A Anna Grassellino %A Kawtar Hafidi %A Zubin Jacob %A Michael McGuigan %A Yannick Meurice %A Zein-Eddine Meziani %A Peter Mueller %A Christine Muschik %A James Osborn %A Matthew Otten %A Peter Petreczky %A Tomas Polakovic %A Alan Poon %A Raphael Pooser %A Alessandro Roggero %A Mark Saffman %A Brent VanDevender %A Jiehang Zhang %A Erez Zohar %Xhis whitepaper is an outcome of the workshop Intersections between Nuclear Physics and Quantum Information held at Argonne National Laboratory on 28-30 March 2018 [www.phy.anl.gov/npqi2018/]. The workshop brought together 116 national and international experts in nuclear physics and quantum information science to explore opportunities for the two fields to collaborate on topics of interest to the U.S. Department of Energy (DOE) Office of Science, Office of Nuclear Physics, and more broadly to U.S. society and industry. The workshop consisted of 22 invited and 10 contributed talks, as well as three panel discussion sessions. Topics discussed included quantum computation, quantum simulation, quantum sensing, nuclear physics detectors, nuclear many-body problem, entanglement at collider energies, and lattice gauge theories.

%8 03/13/2019 %G eng %U https://arxiv.org/abs/1903.05453 %0 Journal Article %J EPTCS %D 2019 %T Parallel Self-Testing of the GHZ State with a Proof by Diagrams %A Spencer Breiner %A Amir Kalev %A Carl Miller %XQuantum self-testing addresses the following question: is it possible to verify the existence of a multipartite state even when one's measurement devices are completely untrusted? This problem has seen abundant activity in the last few years, particularly with the advent of parallel self-testing (i.e., testing several copies of a state at once), which has applications not only to quantum cryptography but also quantum computing. In this work we give the first error-tolerant parallel self-test in a three-party (rather than two-party) scenario, by showing that an arbitrary number of copies of the GHZ state can be self-tested. In order to handle the additional complexity of a three-party setting, we use a diagrammatic proof based on categorical quantum mechanics, rather than a typical symbolic proof. The diagrammatic approach allows for manipulations of the complicated tensor networks that arise in the proof, and gives a demonstration of the importance of picture-languages in quantum information.

%B EPTCS %V 287 %P 43-66 %8 01/29/2019 %G eng %U https://arxiv.org/abs/1806.04744 %R https://doi.org/10.4204/EPTCS.287.3 %0 Journal Article %D 2019 %T Photon pair condensation by engineered dissipation %A Ze-Pei Cian %A Guanyu Zhu %A Su-Kuan Chu %A Alireza Seif %A Wade DeGottardi %A Liang Jiang %A Mohammad Hafezi %XDissipation can usually induce detrimental decoherence in a quantum system. However, engineered dissipation can be used to prepare and stabilize coherent quantum many-body states. Here, we show that by engineering dissipators containing photon pair operators, one can stabilize an exotic dark state, which is a condensate of photon pairs with a phase-nematic order. In this system, the usual superfluid order parameter, i.e. single-photon correlation, is absent, while the photon pair correlation exhibits long-range order. Although the dark state is not unique due to multiple parity sectors, we devise an additional type of dissipators to stabilize the dark state in a particular parity sector via a diffusive annihilation process which obeys Glauber dynamics in an Ising model. Furthermore, we propose an implementation of these photon-pair dissipators in circuit-QED architecture.

%8 04/02/2019 %G eng %U https://arxiv.org/abs/1904.00016 %0 Journal Article %D 2019 %T Polynomial Time Algorithms for Estimating Spectra of Adiabatic Hamiltonians %A Jacob Bringewatt %A William Dorland %A Stephen P. Jordan %XMuch research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians with Hamming symmetric potentials, such as the well studied "spike" example. Due to the large amount of symmetry in these potentials such problems are readily open to analysis both analytically and computationally. However, more realistic potentials do not have such a high degree of symmetry and may have many local minima. Here we present a somewhat more realistic class of problems consisting of many individually Hamming symmetric potential wells. For two or three such wells we demonstrate that such a problem can be solved exactly in time polynomial in the number of qubits and wells. For greater than three wells, we present a tight binding approach with which to efficiently analyze the performance of such Hamiltonians in an adiabatic computation. We provide several basic examples designed to highlight the usefulness of this toy model and to give insight into using the tight binding approach to examining it, including: (1) adiabatic unstructured search with a transverse field driver and a prior guess to the marked item and (2) a scheme for adiabatically simulating the ground states of small collections of strongly interacting spins, with an explicit demonstration for an Ising model Hamiltonian.

%8 05/25/2019 %G eng %U https://arxiv.org/abs/1905.07461 %0 Journal Article %D 2019 %T Quantifying the magic of quantum channels %A Xin Wang %A Mark M. Wilde %A Yuan Su %XTo achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum "magic" or non-stabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimension d, it is known that quantum states with non-negative Wigner function can be efficiently simulated classically. First, inspired by this observation, we introduce a resource theory based on completely positive-Wigner-preserving quantum operations as free operations, and we show that they can be efficiently simulated via a classical algorithm. Second, we introduce two efficiently computable magic measures for quantum channels, called the mana and thauma of a quantum channel. As applications, we show that these measures not only provide fundamental limits on the distillable magic of quantum channels, but they also lead to lower bounds for the task of synthesizing non-Clifford gates. Third, we propose a classical algorithm for simulating noisy quantum circuits, whose sample complexity can be quantified by the mana of a quantum channel. We further show that this algorithm can outperform another approach for simulating noisy quantum circuits, based on channel robustness. Finally, we explore the threshold of non-stabilizerness for basic quantum circuits under depolarizing noise.

%8 2019/03/11 %G eng %U https://arxiv.org/abs/1903.04483 %0 Journal Article %J Phys. Rev. A %D 2019 %T Quantum Algorithm for Simulating the Wave Equation %A Pedro C.S. Costa %A Stephen P. Jordan %A Aaron Ostrander %XWe present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for improved scaling in truncation errors and improved scaling for state preparation relative to general purpose linear differential equation algorithms. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell's equations.

%B Phys. Rev. A %V 99 %8 03/24/2019 %G eng %U https://arxiv.org/abs/1711.05394 %N 012323 %R https://doi.org/10.1103/PhysRevA.99.012323 %0 Journal Article %D 2019 %T Quantum Approximate Optimization with a Trapped-Ion Quantum Simulator %A G. Pagano %A A. Bapat %A P. Becker %A K. S. Collins %A A. De %A P. W. Hess %A H. B. Kaplan %A A. Kyprianidis %A W. L. Tan %A C. Baldwin %A L. T. Brady %A A. Deshpande %A F. Liu %A S. Jordan %A A. V. Gorshkov %A C. Monroe %XQuantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly solving exponentially hard problems, such as optimization and satisfiability. Here we report the first implementation of a shallow-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator to estimate the ground state energy of the transverse field Ising model with tunable long-range interactions. First, we exhaustively search the variational control parameters to approximate the ground state energy with up to 40 trapped-ion qubits. We then interface the quantum simulator with a classical algorithm to more efficiently find the optimal set of parameters that minimizes the resulting energy of the system. We finally sample from the full probability distribution of the QAOA output with single-shot and efficient measurements of every qubit.

%8 06/06/2019 %G eng %U https://arxiv.org/abs/1906.02700 %0 Journal Article %D 2019 %T Quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions %A Freek Witteveen %A Volkher Scholz %A Brian Swingle %A Michael Walter %XThe multiscale entanglement renormalization ansatz describes quantum many-body states by a hierarchical entanglement structure organized by length scale. Numerically, it has been demonstrated to capture critical lattice models and the data of the corresponding conformal field theories with high accuracy. However, a rigorous understanding of its success and precise relation to the continuum is still lacking. To address this challenge, we provide an explicit construction of entanglement-renormalization quantum circuits that rigorously approximate correlation functions of the massless Dirac conformal field theory. We directly target the continuum theory: discreteness is introduced by our choice of how to probe the system, not by any underlying short-distance lattice regulator. To achieve this, we use multiresolution analysis from wavelet theory to obtain an approximation scheme and to implement entanglement renormalization in a natural way. This could be a starting point for constructing quantum circuit approximations for more general conformal field theories.

%8 05/21/2019 %G eng %U https://arxiv.org/abs/1905.08821 %0 Journal Article %D 2019 %T Quantum hardness of learning shallow classical circuits %A Srinivasan Arunachalam %A Alex B. Grilo %A Aarthi Sundaram %XIn this paper we study the quantum learnability of constant-depth classical circuits under the uniform distribution and in the distribution-independent framework of PAC learning. In order to attain our results, we establish connections between quantum learning and quantum-secure cryptosystems. We then achieve the following results. 1) Hardness of learning AC0 and TC0 under the uniform distribution. Our first result concerns the concept class TC0 (resp. AC0), the class of constant-depth and polynomial-sized circuits with unbounded fan-in majority gates (resp. AND, OR, NOT gates). We show that if there exists no quantum polynomial-time (resp. sub-exponential time) algorithm to solve the Learning with Errors (LWE) problem, then there exists no polynomial-time quantum learning algorithm for TC0 (resp. AC0) under the uniform distribution (even with access to quantum membership queries). The main technique in this result uses explicit pseudo-random generators that are believed to be quantum-secure to construct concept classes that are hard to learn quantumly under the uniform distribution. 2) Hardness of learning TC02 in the PAC setting. Our second result shows that if there exists no quantum polynomial time algorithm for the LWE problem, then there exists no polynomial time quantum PAC learning algorithm for the class TC02, i.e., depth-2 TC0 circuits. The main technique in this result is to establish a connection between the quantum security of public-key cryptosystems and the learnability of a concept class that consists of decryption functions of the cryptosystem. This gives a strong conditional negative answer to one of the "Ten Semi-Grand Challenges for Quantum Computing Theory" raised by Aaronson [Aar05], who asked if AC0 and TC0 can be PAC-learned in quantum polynomial time.

%8 03/07/2019 %G eng %U https://arxiv.org/abs/1903.02840 %0 Journal Article %J JHEP04 %D 2019 %T Quantum Lyapunov Spectrum %A Hrant Gharibyan %A Masanori Hanada %A Brian Swingle %A Masaki Tezuka %XWe introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our numerical results suggest that a black hole is not just the fastest scrambler, but also the fastest entropy generator. We also study the statistical features of the quantum Lyapunov spectrum and find universal random matrix behavior, which resembles the recently-found universality in classical chaos. The random matrix behavior is lost when the system is deformed away from chaos, towards integrability or a many-body localized phase. We propose that quantum systems holographically dual to gravity satisfy this universality in a strong form. We further argue that the quantum Lyapunov spectrum contains important additional information beyond the largest Lyapunov exponent and hence provides us with a better characterization of chaos in quantum systems.

%B JHEP04 %V 082 %8 04/10/2019 %G eng %U https://arxiv.org/abs/1809.01671 %R https://doi.org/10.1007/JHEP04(2019)082 %0 Journal Article %D 2019 %T Quantum Physics Meets Music: A "Real-Time" Guitar Recording Using Rydberg-Atoms and Electromagnetically Induced Transparency %A Christopher L. Holloway %A Matthew T. Simons %A Abdulaziz H. Haddab %A Carl J. Williams %A Maxwell W. Holloway %XWe demonstrate how Rydberg atoms and the phenomena of electromagnetically induced transparency can be used to aid in the recording of a musical instrument in real time as it is played. Also, by using two different atomic species (cesium and rubidium) in the same vapor cell, we demonstrate the ability to record two guitars simultaneously, where each atomic species detects and allows for the recording of each guitar separately. The approach shows how audio data (the musical composition) can be detected with a quantum system, illustrating how we can control ensembles of atoms to such an extent that we can use them in this "entertaining" example of recording a musical instrument.

%8 04/01/2019 %G eng %U https://arxiv.org/abs/1904.01952 %0 Journal Article %J New J. Phys. %D 2019 %T Quantum repeaters based on two species trapped ions %A Siddhartha Santra %A Sreraman Muralidharan %A Martin Lichtman %A Liang Jiang %A Christopher Monroe %A Vladimir S. Malinovsky %XWe examine the viability of quantum repeaters based on two-species trapped ion modules for long distance quantum key distribution. Repeater nodes comprised of ion-trap modules of co-trapped ions of distinct species are considered. The species used for communication qubits has excellent optical properties while the other longer lived species serves as a memory qubit in the modules. Each module interacts with the network only via single photons emitted by the communication ions. Coherent Coulomb interaction between ions is utilized to transfer quantum information between the communication and memory ions and to achieve entanglement swapping between two memory ions. We describe simple modular quantum repeater architectures realizable with the ion-trap modules and numerically study the dependence of the quantum key distribution rate on various experimental parameters, including coupling efficiency, gate infidelity, operation time and length of the elementary links. Our analysis suggests crucial improvements necessary in a physical implementation for co-trapped two-species ions to be a competitive platform in long-distance quantum communication.

%B New J. Phys. %V 21 %8 05/02/2019 %G eng %U https://arxiv.org/abs/1811.10723 %N 073002 %R https://doi.org/10.1088/1367-2630/ab2a45 %0 Journal Article %D 2019 %T Quantum spectral methods for differential equations %A Andrew M. Childs %A Jin-Peng Liu %XRecently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a d-dimensional system of linear equations or linear differential equations with complexity poly(logd). While several of these algorithms approximate the solution to within ε with complexity poly(log(1/ε)), no such algorithm was previously known for differential equations with time-dependent coefficients. Here we develop a quantum algorithm for linear ordinary differential equations based on so-called spectral methods, an alternative to finite difference methods that approximates the solution globally. Using this approach, we give a quantum algorithm for time-dependent initial and boundary value problems with complexity poly(logd,log(1/ε)).

%G eng %U https://arxiv.org/abs/1901.00961 %0 Journal Article %D 2019 %T Quantum-inspired classical sublinear-time algorithm for solving low-rank semidefinite programming via sampling approaches %A Nai-Hui Chia %A Tongyang Li %A Han-Hsuan Lin %A Chunhao Wang %XSemidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. Recently, quantum algorithms with superpolynomial speedups for solving SDPs have been proposed assuming access to its constraint matrices in quantum superposition. Mutually inspired by both classical and quantum SDP solvers, in this paper we present a sublinear classical algorithm for solving low-rank SDPs which is asymptotically as good as existing quantum algorithms. Specifically, given an SDP with m constraint matrices, each of dimension n and rank poly(logn), our algorithm gives a succinct description and any entry of the solution matrix in time O(m⋅poly(logn,1/ε)) given access to a sample-based low-overhead data structure of the constraint matrices, where ε is the precision of the solution. In addition, we apply our algorithm to a quantum state learning task as an application. Technically, our approach aligns with both the SDP solvers based on the matrix multiplicative weight (MMW) framework and the recent studies of quantum-inspired machine learning algorithms. The cost of solving SDPs by MMW mainly comes from the exponentiation of Hermitian matrices, and we propose two new technical ingredients (compared to previous sample-based algorithms) for this task that may be of independent interest: ∙ Weighted sampling: assuming sampling access to each individual constraint matrix A1,…,Aτ, we propose a procedure that gives a good approximation of A=A1+⋯+Aτ. ∙ Symmetric approximation: we propose a sampling procedure that gives low-rank spectral decomposition of a Hermitian matrix A. This improves upon previous sampling procedures that only give low-rank singular value decompositions, losing the signs of eigenvalues.

%G eng %U https://arxiv.org/abs/1901.03254 %0 Journal Article %J EPTCS %D 2019 %T ReQWIRE: Reasoning about Reversible Quantum Circuits %A Robert Rand %A Jennifer Paykin %A Dong-Ho Lee %A Steve Zdancewic %XCommon quantum algorithms make heavy use of ancillae: scratch qubits that are initialized at some state and later returned to that state and discarded. Existing quantum circuit languages let programmers assert that a qubit has been returned to the |0> state before it is discarded, allowing for a range of optimizations. However, existing languages do not provide the tools to verify these assertions, introducing a potential source of errors. In this paper we present methods for verifying that ancillae are discarded in the desired state, and use these methods to implement a verified compiler from classical functions to quantum oracles.

%B EPTCS %V 287 %G eng %U https://arxiv.org/abs/1901.10118 %9 In Proceedings QPL 2018, arXiv:1901.09476 %& 299-312 %R https://doi.org/10.4204/EPTCS.287.17 %0 Journal Article %D 2019 %T Resource theory of asymmetric distinguishability for quantum channels %A Xin Wang %A Mark M. Wilde %XThis paper develops the resource theory of asymmetric distinguishability for quantum channels, generalizing the related resource theory for states [arXiv:1006.0302, arXiv:1905.11629]. The key constituents of the channel resource theory are quantum channel boxes, consisting of a pair of quantum channels, which can be manipulated for free by means of an arbitrary quantum superchannel (the most general physical transformation of a quantum channel). One main question of the resource theory is the approximate channel box transformation problem, in which the goal is to transform an initial channel box (or boxes) to a final channel box (or boxes), while allowing for an asymmetric error in the transformation. The channel resource theory is richer than its counterpart for states because there is a wider variety of ways in which this question can be framed, either in the one-shot or n-shot regimes, with the latter having parallel and sequential variants. As in [arXiv:1905.11629], we consider two special cases of the general channel box transformation problem, known as distinguishability distillation and dilution. For the one-shot case, we find that the optimal values of the various tasks are equal to the non-smooth or smooth channel min- or max-relative entropies, thus endowing all of these quantities with operational interpretations. In the asymptotic sequential setting, we prove that the exact distinguishability cost is equal to channel max-relative entropy and the distillable distinguishability is equal to the amortized channel relative entropy of [arXiv:1808.01498]. This latter result can also be understood as a solution to Stein's lemma for quantum channels in the sequential setting. Finally, the theory simplifies significantly for environment-seizable and classical--quantum channel boxes.

%8 07/15/2019 %G eng %U https://arxiv.org/abs/1907.06306 %0 Journal Article %D 2019 %T Resource theory of entanglement for bipartite quantum channels %A Stefan Bäuml %A Siddhartha Das %A Xin Wang %A Mark M. Wilde %XThe traditional perspective in quantum resource theories concerns how to use free operations to convert one resourceful quantum state to another one. For example, a fundamental and well known question in entanglement theory is to determine the distillable entanglement of a bipartite state, which is equal to the maximum rate at which fresh Bell states can be distilled from many copies of a given bipartite state by employing local operations and classical communication for free. It is the aim of this paper to take this kind of question to the next level, with the main question being: What is the best way of using free channels to convert one resourceful quantum channel to another? Here we focus on the the resource theory of entanglement for bipartite channels and establish several fundamental tasks and results regarding it. In particular, we establish bounds on several pertinent information processing tasks in channel entanglement theory, and we define several entanglement measures for bipartite channels, including the logarithmic negativity and the κ-entanglement. We also show that the max-Rains information of [Bäuml et al., Physical Review Letters, 121, 250504 (2018)] has a divergence interpretation, which is helpful for simplifying the results of this earlier work.

%8 07/08/2019 %G eng %U https://arxiv.org/abs/1907.04181 %0 Journal Article %J Phys. Rev. Lett %D 2019 %T Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator %A Su-Kuan Chu %A Guanyu Zhu %A James R. Garrison %A Zachary Eldredge %A Ana Valdés Curiel %A Przemyslaw Bienias %A I. B. Spielman %A Alexey V. Gorshkov %XThe multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.

%B Phys. Rev. Lett %V 122 %8 03/27/2019 %G eng %U https://arxiv.org/abs/1807.11486 %N 120502 %R https://doi.org/10.1103/PhysRevLett.122.120502 %0 Journal Article %D 2019 %T Signaling and Scrambling with Strongly Long-Range Interactions %A Andrew Y. Guo %A Minh C. Tran %A Andrew M. Childs %A Alexey V. Gorshkov %A Zhe-Xuan Gong %XStrongly long-range interacting quantum systems---those with interactions decaying as a power-law 1/rα in the distance r on a D-dimensional lattice for α≤D---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for α≤D/2. Our second bound pertains to generic long-range interacting spin Hamiltonians, and leads to a tight lower bound for the signaling time to extensive subsets of the system for all α<D. This result also lower-bounds the scrambling time, and suggests a path towards achieving a tight scrambling bound that can prove the long-standing fast scrambling conjecture.

%8 06/06/2019 %G eng %U https://arxiv.org/abs/1906.02662 %0 Journal Article %D 2019 %T Simulating large quantum circuits on a small quantum computer %A Tianyi Peng %A Aram Harrow %A Maris Ozols %A Xiaodi Wu %XLimited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters K and d of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most d with at most K qubits of inter-cluster quantum communication. Our main result is a simulation scheme of any (K,d)-clustered quantum circuit on a d-qubit machine in time roughly 2O(K). An important application of our result is the simulation of clustered quantum systems---such as large molecules---that can be partitioned into multiple significantly smaller clusters with weak interactions among them. Another potential application is quantum optimization: we demonstrate numerically that variational quantum eigensolvers can still perform well when restricted to clustered circuits, thus making it feasible to study large quantum systems on small quantum devices.

%8 03/29/2019 %G eng %U https://arxiv.org/abs/1904.00102 %0 Journal Article %D 2019 %T Simulating quantum circuits by classical circuits %A Daochen Wang %XIn a recent breakthrough, Bravyi, Gosset and König (BGK) [Science, 2018] proved that "simulating" constant depth quantum circuits takes classical circuits Ω(logn) depth. In our paper, we first formalise their notion of simulation, which we call "possibilistic simulation". Then, from well-known results, we deduce that their circuits can be simulated in depth O(log2n). Separately, we construct explicit classical circuits that can simulate any depth-d quantum circuit with Clifford and t T-gates in depth O(d+t). Our classical circuits use {NOT, AND, OR} gates of fan-in ≤2.

%8 04/10/2019 %G eng %U https://arxiv.org/abs/1904.05282 %0 Journal Article %D 2019 %T Statistical Privacy in Distributed Average Consensus on Bounded Real Inputs %A Nirupam Gupta %A Jonathan Katz %A Nikhil Chopra %XThis paper proposes a privacy protocol for distributed average consensus algorithms on bounded real-valued inputs that guarantees statistical privacy of honest agents' inputs against colluding (passive adversarial) agents, if the set of colluding agents is not a vertex cut in the underlying communication network. This implies that privacy of agents' inputs is preserved against t number of arbitrary colluding agents if the connectivity of the communication network is at least (t+1). A similar privacy protocol has been proposed for the case of bounded integral inputs in our previous paper~\cite{gupta2018information}. However, many applications of distributed consensus concerning distributed control or state estimation deal with real-valued inputs. Thus, in this paper we propose an extension of the privacy protocol in~\cite{gupta2018information}, for bounded real-valued agents' inputs, where bounds are known apriori to all the agents.

%8 03/20/2019 %G eng %U https://arxiv.org/abs/1903.09315 %0 Journal Article %D 2019 %T Sublinear quantum algorithms for training linear and kernel-based classifiers %A Tongyang Li %A Shouvanik Chakrabarti %A Xiaodi Wu %XWe investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given n d-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training classifiers with constant margin runs in O~(n+d) time. We design sublinear quantum algorithms for the same task running in O~(n−−√+d−−√) time, a quadratic improvement in both n and d. Moreover, our algorithms use the standard quantization of the classical input and generate the same classical output, suggesting minimal overheads when used as subroutines for end-to-end applications. We also demonstrate a tight lower bound (up to poly-log factors) and discuss the possibility of implementation on near-term quantum machines. As a side result, we also give sublinear quantum algorithms for approximating the equilibria of n-dimensional matrix zero-sum games with optimal complexity Θ~(n−−√).

%8 04/03/2019 %G eng %U https://arxiv.org/abs/1904.02276 %0 Journal Article %J Phys. Rev. D %D 2019 %T Thermalization and chaos in QED3 %A Julia Steinberg %A Brian Swingle %XWe study the real time dynamics of NF flavors of fermions coupled to a U(1) gauge field in 2+1 dimensions to leading order in a 1/NF expansion. For large enough NF, this is an interacting conformal field theory and describes the low energy properties of the Dirac spin liquid. We focus on thermalization and the onset of many-body quantum chaos which can be diagnosed from the growth of initally anti-commuting fermion field operators. We compute such anti-commutators in this gauge theory to leading order in 1/NF. We find that the anti-commutator grows exponentially in time and compute the quantum Lyapunov exponent. We briefly comment on chaos, locality, and gauge invariance.

%B Phys. Rev. D %V 99 %8 04/11/2019 %G eng %U https://arxiv.org/abs/1901.04984 %N 076007 %R https://doi.org/10.1103/PhysRevD.99.076007 %0 Journal Article %D 2019 %T Time-dependent Hamiltonian simulation with L1-norm scaling %A Dominic W. Berry %A Andrew M. Childs %A Yuan Su %A Xin Wang %A Nathan Wiebe %XThe difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For the case of sparse Hamiltonian simulation, the gate complexity scales with the L1 norm ∫t0dτ∥H(τ)∥max, whereas the best previous results scale with tmaxτ∈[0,t]∥H(τ)∥max. We also show analogous results for Hamiltonians that are linear combinations of unitaries. Our approaches thus provide an improvement over previous simulation algorithms that can be substantial when the Hamiltonian varies significantly. We introduce two new techniques: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schrödinger equation. The rescaled Dyson-series algorithm is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation. By leveraging the L1-norm information, we obtain polynomial speedups for semi-classical simulations of scattering processes in quantum chemistry.

%8 06/17/2019 %G eng %U https://arxiv.org/abs/1906.07115 %0 Journal Article %D 2019 %T Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point %A Michael Schuler %A Stephan Hesselmann %A Seth Whitsitt %A Thomas C. Lang %A Stefan Wessel %A Andreas M. Läuchli %XWe establish the universal torus low-energy spectra at the free Dirac fixed point and at the strongly coupled {\em chiral Ising} fixed point and their subtle crossover behaviour in the Gross-Neuveu-Yukawa field theory with nD=4 component Dirac spinors in D=(2+1) dimensions. These fixed points and the field theories are directly relevant for the long-wavelength physics of certain interacting Dirac systems, such as repulsive spinless fermions on the honeycomb lattice or π-flux square lattice. The torus spectrum has been shown previously to serve as a characteristic fingerprint of relativistic fixed points and is a powerful tool to discriminate quantum critical behaviour in numerical simulations. Here we use a combination of exact diagonalization and quantum Monte Carlo simulations of strongly interacting fermionic lattice models, to compute the critical energy spectrum on finite-size clusters with periodic boundaries and extrapolate them to the thermodynamic limit. Additionally, we compute the torus spectrum analytically using the perturbative expansion in ε=4−D, which is in good agreement with the numerical results, thereby validating the presence of the chiral Ising fixed point in the lattice models at hand. We show that the strong interaction between the spinor field and the scalar order-parameter field strongly influences the critical torus spectrum. Building on these results we are able to address the subtle crossover physics of the low-energy spectrum flowing from the chiral Ising fixed point to the Dirac fixed point, and analyze earlier flawed attempts to extract Fermi velocity renormalizations from the low-energy spectrum

%8 07/11/2019 %G eng %U https://arxiv.org/abs/1907.05373 %0 Journal Article %D 2019 %T Toward convergence of effective field theory simulations on digital quantum computers %A Omar Shehab %A Kevin A. Landsman %A Yunseong Nam %A Daiwei Zhu %A Norbert M. Linke %A Matthew J. Keesan %A Raphael C. Pooser %A Christopher R. Monroe %XWe report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansaetze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of E4=−2.220±0.179MeV may be compared with the exact Deuteron ground-state energy −2.224MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps for the first time. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.

%8 04/18/2019 %G eng %U https://arxiv.org/abs/1904.04338 %0 Journal Article %D 2019 %T Towards Bulk Metric Reconstruction from Extremal Area Variations %A Ning Bao %A ChunJun Cao %A Sebastian Fischetti %A Cynthia Keeler %XThe Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension , knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an\textit {explicit} spacetime metric reconstruction.

%8 04/09/19 %G eng %U https://arxiv.org/abs/1904.04834 %0 Journal Article %D 2019 %T Two-qubit entangling gates within arbitrarily long chains of trapped ions %A Kevin A. Landsman %A Yukai Wu %A Pak Hong Leung %A Daiwei Zhu %A Norbert M. Linke %A Kenneth R. Brown %A Luming Duan %A Christopher R. Monroe %XIon trap systems are a leading platform for large scale quantum computers. Trapped ion qubit crystals are fully-connected and reconfigurable, owing to their long range Coulomb interaction that can be modulated with external optical forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals, simplifying the scaling of ion trap quantum computers. To this end, we present analytical work that determines how parallel entangling gates produce a crosstalk error that falls off as the inverse cube of the distance between the pairs. We also show experimental work demonstrating entangling gates on a fully-connected chain of seventeen 171Yb+ ions with fidelities as high as 97(1)%.

%8 05/28/2019 %G eng %U https://arxiv.org/abs/1905.10421 %0 Journal Article %J Quantum %D 2019 %T Variational Quantum Computation of Excited States %A Oscar Higgott %A Daochen Wang %A Stephen Brierley %XThe calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited state energies and their degeneracies. We propose an implementation that requires the same number of qubits as VQE and at most twice the circuit depth. Our method is robust to control errors, is compatible with error-mitigation strategies and can be implemented on near-term quantum compute

%B Quantum %V 3 %8 06/28/2019 %G eng %U https://arxiv.org/abs/1805.08138 %N 156 %R https://doi.org/10.22331/q-2019-07-01-156 %0 Journal Article %D 2019 %T Verification Logics for Quantum Programs %A Robert Rand %XWe survey the landscape of Hoare logics for quantum programs. We review three papers: "Reasoning about imperative quantum programs" by Chadha, Mateus and Sernadas; "A logic for formal verification of quantum programs" by Yoshihiko Kakutani; and "Floyd-hoare logic for quantum programs" by Mingsheng Ying. We compare the mathematical foundations of the logics, their underlying languages, and the expressivity of their assertions. We also use the languages to verify the Deutsch-Jozsa Algorithm, and discuss their relative usability in practice.

%G eng %U https://arxiv.org/abs/1904.04304 %9 Originally submitted in March 2016 as a qualifying examination (WPE-II) for the PhD program at the University of Pennsylvania %0 Journal Article %D 2019 %T Verified Optimization in a Quantum Intermediate Representation %A Kesha Hietala %A Robert Rand %A Shih-Han Hung %A Xiaodi Wu %A Michael Hicks %XWe present sqire, a low-level language for quantum computing and verification. sqire uses a global register of quantum bits, allowing easy compilation to and from existing `quantum assembly' languages and simplifying the verification process. We demonstrate the power of sqire as an intermediate representation of quantum programs by verifying a number of useful optimizations, and we demonstrate sqire's use as a tool for general verification by proving several quantum programs correct.

%8 04/12/2019 %G eng %U https://arxiv.org/abs/1904.06319 %0 Journal Article %D 2019 %T α-Logarithmic negativity %A Xin Wang %A Mark M. Wilde %XThe logarithmic negativity of a bipartite quantum state is a widely employed entanglement measure in quantum information theory, due to the fact that it is easy to compute and serves as an upper bound on distillable entanglement. More recently, the κ-entanglement of a bipartite state was shown to be the first entanglement measure that is both easily computable and operationally meaningful, being equal to the exact entanglement cost of a bipartite quantum state when the free operations are those that completely preserve the positivity of the partial transpose. In this paper, we provide a non-trivial link between these two entanglement measures, by showing that they are the extremes of an ordered family of α-logarithmic negativity entanglement measures, each of which is identified by a parameter α∈[1,∞]. In this family, the original logarithmic negativity is recovered as the smallest with α=1, and the κ-entanglement is recovered as the largest with α=∞. We prove that the α-logarithmic negativity satisfies the following properties: entanglement monotone, normalization, faithfulness, and subadditivity. We also prove that it is neither convex nor monogamous. Finally, we define the α-logarithmic negativity of a quantum channel as a generalization of the notion for quantum states, and we show how to generalize many of the concepts to arbitrary resource theories.

%8 04/23/2019 %G eng %U https://arxiv.org/abs/1904.10437 %0 Journal Article %J Physical Review B %D 2018 %T Absence of Thermalization in Finite Isolated Interacting Floquet Systems %A Karthik Seetharam %A Paraj Titum %A Michael Kolodrubetz %A Gil Refael %XConventional wisdom suggests that the long time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy non-thermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit non-thermal behavior due to finite system size. We consider a one-dimensional system of spinless fermions with nearest-neighbor interactions where the interaction term is driven. Interestingly, even with no static component of the interaction, the quasienergy spectrum contains gaps and a significant fraction of the Floquet eigenstates, at all quasienergies, have non-thermal average doublon densities. We show that this non-thermal behavior arises due to emergent integrability at large interaction strength and discuss how the integrability breaks down with power-law behavior in system size.

%B Physical Review B %V 97 %P 014311 %8 2018/01/29 %G eng %U https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.014311 %N 1 %R 10.1103/PhysRevB.97.014311 %0 Journal Article %D 2018 %T Accessing scrambling using matrix product operators %A Shenglong Xu %A Brian Swingle %XScrambling, a process in which quantum information spreads over a complex quantum system becoming inaccessible to simple probes, happens in generic chaotic quantum many-body systems, ranging from spin chains, to metals, even to black holes. Scrambling can be measured using out-of-time-ordered correlators (OTOCs), which are closely tied to the growth of Heisenberg operators. In this work, we present a general method to calculate OTOCs of local operators in local one-dimensional systems based on approximating Heisenberg operators as matrix-product operators (MPOs). Contrary to the common belief that such tensor network methods work only at early times, we show that the entire early growth region of the OTOC can be captured using an MPO approximation with modest bond dimension. We analytically establish the goodness of the approximation by showing that if an appropriate OTOC is close to its initial value, then the associated Heisenberg operator has low entanglement across a given cut. We use the method to study scrambling in a chaotic spin chain with 201 sites. Based on this data and OTOC results for black holes, local random circuit models, and non-interacting systems, we conjecture a universal form for the dynamics of the OTOC near the wavefront. We show that this form collapses the chaotic spin chain data over more than fifteen orders of magnitude.

%G eng %U https://arxiv.org/abs/1802.00801 %0 Journal Article %D 2018 %T Approximate Quantum Fourier Transform with O(nlog(n)) T gates %A Yunseong Nam %A Yuan Su %A Dmitri Maslov %XThe ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer enables the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete logarithm over Abelian groups, and phase estimation. The standard fault-tolerant implementation of an n-qubit QFT approximates the desired transformation by removing small-angle controlled rotations and synthesizing the remaining ones into Clifford+t gates, incurring the t-count complexity of O(n log2 (n)). In this paper we show how to obtain approximate QFT with the t-count of O(n log(n)). Our approach relies on quantum circuits with measurements and feedforward, and on reusing a special quantum state that induces the phase gradient transformation. We report asymptotic analysis as well as concrete circuits, demonstrating significant advantages in both theory and practice.

%8 2018/03/13 %G eng %U https://arxiv.org/abs/1803.04933 %0 Journal Article %J Phys. Rev. Lett %D 2018 %T Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics %A Fangli Liu %A James R. Garrison %A Dong-Ling Deng %A Zhe-Xuan Gong %A Alexey V. Gorshkov %XWe study the non-equilibrium dynamics of Abelian anyons in a one-dimensional system. We find that the interplay of anyonic statistics and interactions gives rise to spatially asymmetric particle transport together with a novel dynamical symmetry that depends on the anyonic statistical angle and the sign of interactions. Moreover, we show that anyonic statistics induces asymmetric spreading of quantum information, characterized by asymmetric light cones of out-of-time-ordered correlators. Such asymmetric dynamics is in sharp contrast with the dynamics of conventional fermions or bosons, where both the transport and information dynamics are spatially symmetric. We further discuss experiments with cold atoms where the predicted phenomena can be observed using state-of-the-art technologies. Our results pave the way toward experimentally probing anyonic statistics through non-equilibrium dynamics.

%B Phys. Rev. Lett %V 121 %8 2018/12/20 %G eng %U https://arxiv.org/abs/1809.02614 %N 250404 %R https://doi.org/10.1103/PhysRevLett.121.250404 %0 Journal Article %J npj:Quantum Information %D 2018 %T Automated optimization of large quantum circuits with continuous parameters %A Yunseong Nam %A Neil J. Ross %A Yuan Su %A Andrew M. Childs %A Dmitri Maslov %XWe develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection of fast algorithms capable of optimizing large-scale quantum circuits. For the suite of benchmarks considered, we obtain substantial reductions in gate counts. In particular, we provide better optimization in significantly less time than previous approaches, while making minimal structural changes so as to preserve the basic layout of the underlying quantum algorithms. Our results help bridge the gap between the computations that can be run on existing hardware and those that are expected to outperform classical computers.

%B npj:Quantum Information %V 4 %8 2017/10/19 %G eng %U https://arxiv.org/abs/1710.07345 %N 23 %R https://doi.org/10.1038/s41534-018-0072-4 %0 Journal Article %D 2018 %T An autonomous single-piston engine with a quantum rotor %A Alexandre Roulet %A Stefan Nimmrichter %A Jacob M. Taylor %XPistons are elementary components of a wide variety of thermal engines, converting input fuel into rotational motion. Here, we propose a single-piston engine where the rotational degree of freedom is effectively realized by the flux of a superconducting island -- a quantum rotor -- while the working volume corresponds to the effective length of a superconducting resonator. Our autonomous design implements a Carnot cycle, relies solely on standard thermal baths and can be implemented with circuit quantum electrodynamics. We demonstrate how the piston is able to extract a net positive work via its built-in synchronicity using a filter cavity as an effective valve, eliminating the need for external control.

%8 2018/02/15 %G eng %U https://arxiv.org/abs/1802.05486 %R https://doi.org/10.1088/2058-9565/aac40d %0 Journal Article %D 2018 %T Bang-bang control as a design principle for classical and quantum optimization algorithms %A Aniruddha Bapat %A Stephen Jordan %XPhysically motivated classical heuristic optimization algorithms such as simulated annealing (SA) treat the objective function as an energy landscape, and allow walkers to escape local minima. It has been argued that quantum properties such as tunneling may give quantum algorithms advantage in finding ground states of vast, rugged cost landscapes. Indeed, the Quantum Adiabatic Algorithm (QAO) and the recent Quantum Approximate Optimization Algorithm (QAOA) have shown promising results on various problem instances that are considered classically hard. Here, we argue that the type of control strategy used by the optimization algorithm may be crucial to its success. Along with SA, QAO and QAOA, we define a new, bang-bang version of simulated annealing, BBSA, and study the performance of these algorithms on two well-studied problem instances from the literature. Both classically and quantumly, the successful control strategy is found to be bang-bang, exponentially outperforming the quasistatic analogues on the same instances. Lastly, we construct O(1)-depth QAOA protocols for a class of symmetric cost functions, and provide an accompanying physical picture.

%G eng %U https://arxiv.org/abs/1812.02746 %0 Journal Article %D 2018 %T A belief propagation algorithm based on domain decomposition %A Brad Lackey %XThis note provides a detailed description and derivation of the domain decomposition algorithm that appears in previous works by the author. Given a large re-estimation problem, domain decomposition provides an iterative method for assembling Boltzmann distributions associated to small subproblems into an approximation of the Bayesian posterior of the whole problem. The algorithm is amenable to using Boltzmann sampling to approximate these Boltzmann distributions. In previous work, we have shown the capability of heuristic versions of this algorithm to solve LDPC decoding and circuit fault diagnosis problems too large to fit on quantum annealing hardware used for sampling. Here, we rigorously prove soundness of the method.

%G eng %U https://arxiv.org/abs/1810.10005 %0 Journal Article %D 2018 %T Bell monogamy relations in arbitrary qubit networks %A Minh Cong Tran %A Ravishankar Ramanathan %A Matthew McKague %A Dagomir Kaszlikowski %A Tomasz Paterek %XCharacterizing trade-offs between simultaneous violations of multiple Bell inequalities in a large network of qubits is computationally demanding. We propose a graph-theoretic approach to efficiently produce Bell monogamy relations in arbitrary arrangements of qubits. All the relations obtained for bipartite Bell inequalities are tight and leverage only a single Bell monogamy relation. This feature is unique to bipartite Bell inequalities, as we show that there is no finite set of such elementary monogamy relations for multipartite inequalities. Nevertheless, many tight monogamy relations for multipartite inequalities can be obtained with our method as shown in explicit examples.

%8 2018/01/09 %G eng %U https://arxiv.org/abs/1801.03071 %R https://doi.org/10.1103/PhysRevA.98.052325 %0 Journal Article %D 2018 %T Black Hole Microstate Cosmology %A Sean Cooper %A Moshe Rozali %A Brian Swingle %A Mark Van Raamsdonk %A Christopher Waddell %A David Wakeham %XIn this note, we explore the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a geometrical behind-the-horizon region, modelled by a portion of a second asymptotic region terminating at an end-of-the-world (ETW) brane. We study the time-dependent physics of this behind-the-horizon region, whose ETW boundary geometry takes the form of a closed FRW spacetime. We show that in many cases, this behind-the-horizon physics can be probed directly by looking at the time dependence of entanglement entropy for sufficiently large spatial CFT subsystems. We study in particular states defined via Euclidean evolution from conformal boundary states and give specific predictions for the behavior of the entanglement entropy in this case. We perform analogous calculations for the SYK model and find qualitative agreement with our expectations. A fascinating possibility is that for certain states, we might have gravity localized to the ETW brane as in the Randall-Sundrum II scenario for cosmology. In this case, the effective description of physics beyond the horizon could be a big bang/big crunch cosmology of the same dimensionality as the CFT. In this case, the d-dimensional CFT describing the black hole microstate would give a precise, microscopic description of the d-dimensional cosmological physics.

%G eng %U https://arxiv.org/abs/1810.10601 %0 Journal Article %D 2018 %T Blind quantum computation using the central spin Hamiltonian %A Minh Cong Tran %A Jacob M. Taylor %XBlindness is a desirable feature in delegated computation. In the classical setting, blind computations protect the data or even the program run by a server. In the quantum regime, blind computing may also enable testing computational or other quantum properties of the server system. Here we propose a scheme for universal blind quantum computation using a quantum simulator capable of emulating Heisenberg-like Hamiltonians. Our scheme is inspired by the central spin Hamiltonian in which a single spin controls dynamics of a number of bath spins. We show how, by manipulating this spin, a client that only accesses the central spin can effectively perform blind computation on the bath spins. Remarkably, two-way quantum communication mediated by the central spin is sufficient to ensure security in the scheme. Finally, we provide explicit examples of how our universal blind quantum computation enables verification of the power of the server from classical to stabilizer to full BQP computation.

%8 2018/01/11 %G eng %U https://arxiv.org/abs/1801.04006 %0 Journal Article %D 2018 %T Bose Condensation of Photons Thermalized via Laser Cooling of Atoms %A Chiao-Hsuan Wang %A M. J. Gullans %A J. V. Porto %A William D. Phillips %A Jacob M. Taylor %XA Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low temperatures. Photons, one of the most prominent species of bosons, do not typically condense due to the lack of a particle number-conservation. We recently described a photon thermalization mechanism which gives rise to a grand canonical ensemble of light with effective photon number conservation between a subsystem and a particle reservoir. This mechanism occurs during Doppler laser cooling of atoms where the atoms serve as a temperature reservoir while the cooling laser photons serve as a particle reservoir. Here we address the question of the possibility of a BEC of photons in this laser cooling photon thermalization scenario and theoretically demonstrate that a Bose condensation of photons can be realized by cooling an ensemble of two-level atoms (realizable with alkaline earth atoms) inside a Fabry-Perot cavity.

%G eng %U https://arxiv.org/abs/1809.07777 %0 Journal Article %J Quantum %D 2018 %T BQP-completeness of Scattering in Scalar Quantum Field Theory %A Stephen P. Jordan %A Hari Krovi %A Keith S. M. Lee %A John Preskill %XRecent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.

%B Quantum %V 2 %P 44 %8 2018/01/08 %G eng %U https://quantum-journal.org/papers/q-2018-01-08-44/ %R 10.22331/q-2018-01-08-44 %0 Journal Article %D 2018 %T Can you sign a quantum state? %A Gorjan Alagic %A Tommaso Gagliardoni %A Christian Majenz %XCryptography with quantum states exhibits a number of surprising and counterintuitive features. In a 2002 work, Barnum et al. argued informally that these strange features should imply that digital signatures for quantum states are impossible (Barnum et al., FOCS 2002). In this work, we perform the first rigorous study of the problem of signing quantum states. We first show that the intuition of Barnum et al. was correct, by proving an impossibility result which rules out even very weak forms of signing quantum states. Essentially, we show that any non-trivial combination of correctness and security requirements results in negligible security. This rules out all quantum signature schemes except those which simply measure the state and then sign the outcome using a classical scheme. In other words, only classical signature schemes exist. We then show a positive result: it is possible to sign quantum states, provided that they are also encrypted with the public key of the intended recipient. Following classical nomenclature, we call this notion quantum signcryption. Classically, signcryption is only interesting if it provides superior efficiency to simultaneous encryption and signing. Our results imply that, quantumly, it is far more interesting: by the laws of quantum mechanics, it is the only signing method available. We develop security definitions for quantum signcryption, ranging from a simple one-time two-user setting, to a chosen-ciphertext-secure many-time multi-user setting. We also give secure constructions based on post-quantum public-key primitives. Along the way, we show that a natural hybrid method of combining classical and quantum schemes can be used to "upgrade" a secure classical scheme to the fully-quantum setting, in a wide range of cryptographic settings including signcryption, authenticated encryption, and chosen-ciphertext security.

%G eng %U https://arxiv.org/abs/1811.11858 %0 Journal Article %D 2018 %T Canonical forms for single-qutrit Clifford+T operators %A Andrew N. Glaudell %A Neil J. Ross %A Jacob M. Taylor %XWe introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. We show that our canonical forms are T-optimal in the sense that among all the single-qutrit Clifford+T circuits implementing a given operator our canonical form uses the least number of T gates. Finally, we provide an algorithm which inputs the description of an operator (as a matrix or a circuit) and constructs the canonical form for this operator. The algorithm runs in time linear in the number of T gates. Our results provide a higher-dimensional generalization of prior work by Matsumoto and Amano who introduced similar canonical forms for single-qubit Clifford+T circuits.

%G eng %U https://arxiv.org/abs/1803.05047 %0 Conference Paper %B Annual ACM Symposium on the Theory of Computing STOC 2018 %D 2018 %T Capacity Approaching Codes for Low Noise Interactive Quantum Communication %A Debbie Leung %A Ashwin Nayak %A Ala Shayeghi %A Dave Touchette %A Penghui Yao %A Nengkun Yu %XWe consider the problem of implementing two-party interactive quantum

communication over noisy channels, a necessary endeavor if we wish to

fully reap quantum advantages for communication.

For an arbitrary protocol with n messages, designed for

noiseless qudit channels, our main result is a simulation method that fails with probability less than

$2^{-\Theta(n\epsilon)}$ and uses a qudit channel $n(1 + \Theta

(\sqrt{\epsilon}))$ times, of which an $\epsilon$ fraction can be

corrupted adversarially.

The simulation is thus capacity achieving to leading order, and

we conjecture that it is optimal up to a constant factor in

the $\sqrt{\epsilon}$ term.

Furthermore, the simulation is in a model that does not require

pre-shared resources such as randomness or entanglement between the

communicating parties.

Surprisingly, this outperforms the best-known overhead of $1 +

O(\sqrt{\epsilon \log \log 1/\epsilon})$ in the corresponding

\emph{classical} model, which is also conjectured to be optimal

[Haeupler, FOCS'14].

Our work also improves over the best previously known quantum result

where the overhead is a non-explicit large constant [Brassard \emph{et

al.}, FOCS'14] for low $\epsilon$.

%B Annual ACM Symposium on the Theory of Computing STOC 2018
%8 2018/01/01
%G eng
%U http://acm-stoc.org/stoc2018/STOC-2018-Accepted.html
%0 Journal Article
%J Phys. Rev. B 98, 060501
%D 2018
%T Circuit QED-based measurement of vortex lattice order in a Josephson junction array
%A R. Cosmic
%A Hiroki Ikegami
%A Zhirong Lin
%A Kunihiro Inomata
%A Jacob M. Taylor
%A Yasunobu Nakamura
%X Superconductivity provides a canonical example of a quantum phase of matter. When superconducting islands are connected by Josephson junctions in a lattice, the low temperature state of the system can map to the celebrated XY model and its associated universality classes. This has been used to experimentally implement realizations of Mott insulator and Berezinskii--Kosterlitz--Thouless (BKT) transitions to vortex dynamics analogous to those in type-II superconductors. When an external magnetic field is added, the effective spins of the XY model become frustrated, leading to the formation of topological defects (vortices). Here we observe the many-body dynamics of such an array, including frustration, via its coupling to a superconducting microwave cavity. We take the design of the transmon qubit, but replace the single junction between two antenna pads with the complete array. This allows us to probe the system at 10 mK with minimal self-heating by using weak coherent states at the single (microwave) photon level to probe the resonance frequency of the cavity. We observe signatures of ordered vortex lattice at rational flux fillings of the array.

%B Phys. Rev. B 98, 060501 %8 2018/03/12 %G eng %U https://arxiv.org/abs/1803.04113 %R https://doi.org/10.1103/PhysRevB.98.060501 %0 Journal Article %D 2018 %T Classical lower bounds from quantum upper bounds %A Shalev Ben-David %A Adam Bouland %A Ankit Garg %A Robin Kothari %XWe prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the combinatorial group testing problem.

We show that for any function f, the approximate degree of computing the OR of n copies of f is Omega(sqrt{n}) times the approximate degree of f, which is optimal. No such general result was known prior to our work, and even the lower bound for the OR of ANDs function was only resolved in 2013.

We then prove an analogous result in communication complexity, showing that the logarithm of the approximate rank (or more precisely, the approximate gamma_2 norm) of F: X x Y -> {0,1} grows by a factor of Omega~(sqrt{n}) when we take the OR of n copies of F, which is also essentially optimal. As a corollary, we give a new proof of Razborov's celebrated Omega(sqrt{n}) lower bound on the quantum communication complexity of the disjointness problem.

Finally, we generalize both these results from composition with the OR function to composition with arbitrary symmetric functions, yielding nearly optimal lower bounds in this setting as well.

There has been a recent surge of interest and progress in creating subwavelength free-space optical potentials for ultra-cold atoms. A key open question is whether geometric potentials, which are repulsive and ubiquitous in the creation of subwavelength free-space potentials, forbid the creation of narrow traps with long lifetimes. Here, we show that it is possible to create such traps. We propose two schemes for realizing subwavelength traps and demonstrate their superiority over existing proposals. We analyze the lifetime of atoms in such traps and show that long-lived bound states are possible. This work opens a new frontier for the subwavelength control and manipulation of ultracold matter, with applications in quantum chemistry and quantum simulation.

%G eng %U https://arxiv.org/abs/1808.02487 %0 Journal Article %J Nature %D 2018 %T A Coherent Spin-Photon Interface in Silicon %A X. Mi %A M. Benito %A S. Putz %A D. M. Zajac %A J. M. Taylor %A Guido Burkard %A J. R. Petta %XElectron spins in silicon quantum dots are attractive systems for quantum computing due to their long coherence times and the promise of rapid scaling using semiconductor fabrication techniques. While nearest neighbor exchange coupling of two spins has been demonstrated, the interaction of spins via microwave frequency photons could enable long distance spin-spin coupling and "all-to-all" qubit connectivity. Here we demonstrate strong-coupling between a single spin in silicon and a microwave frequency photon with spin-photon coupling rates g_s/(2π) > 10 MHz. The mechanism enabling coherent spin-photon interactions is based on spin-charge hybridization in the presence of a magnetic field gradient. In addition to spin-photon coupling, we demonstrate coherent control of a single spin in the device and quantum non-demolition spin state readout using cavity photons. These results open a direct path toward entangling single spins using microwave frequency photons.

%B Nature %V 555 %P 599-603 %8 2018/03/29 %G eng %U https://arxiv.org/abs/1710.03265 %R https://doi.org/10.1038/nature25769 %0 Journal Article %J Nature %D 2018 %T A coherent spin–photon interface in silicon %A X. Mi %A M. Benito %A S. Putz %A D. M. Zajac %A J. M. Taylor %A Guido Burkard %A J. R. Petta %XElectron spins in silicon quantum dots are attractive systems for quantum computing owing to their long coherence times and the promise of rapid scaling of the number of dots in a system using semiconductor fabrication techniques. Although nearest-neighbour exchange coupling of two spins has been demonstrated, the interaction of spins via microwave-frequency photons could enable long-distance spin–spin coupling and connections between arbitrary pairs of qubits (‘all-to-all’ connectivity) in a spin-based quantum processor. Realizing coherent spin–photon coupling is challenging because of the small magnetic-dipole moment of a single spin, which limits magnetic-dipole coupling rates to less than 1 kilohertz. Here we demonstrate strong coupling between a single spin in silicon and a single microwave-frequency photon, with spin–photon coupling rates of more than 10 megahertz. The mechanism that enables the coherent spin–photon interactions is based on spin–charge hybridization in the presence of a magnetic-field gradient. In addition to spin–photon coupling, we demonstrate coherent control and dispersive readout of a single spin. These results open up a direct path to entangling single spins using microwave-frequency photons.

%B Nature %8 2018/02/14 %G eng %U https://www.nature.com/articles/nature25769#author-information %R 10.1038/nature25769 %0 Journal Article %D 2018 %T Cryogenic Trapped-Ion System for Large Scale Quantum Simulation %A G. Pagano %A P. W. Hess %A H. B. Kaplan %A W. L. Tan %A P. Richerme %A P. Becker %A A. Kyprianidis %A J. Zhang %A E. Birckelbaw %A M. R. Hernandez %A Y. Wu %A C. Monroe %XWe present a cryogenic ion trapping system designed for large scale quantum simulation of spin models. Our apparatus is based on a segmented-blade ion trap enclosed in a 4 K cryostat, which enables us to routinely trap over 100 171Yb+ ions in a linear configuration for hours due to a low background gas pressure from differential cryo-pumping. We characterize the cryogenic vacuum by using trapped ion crystals as a pressure gauge, measuring both inelastic and elastic collision rates with the molecular background gas. We demonstrate nearly equidistant ion spacing for chains of up to 44 ions using anharmonic axial potentials. This reliable production and lifetime enhancement of large linear ion chains will enable quantum simulation of spin models that are intractable with classical computer modelling.

%G eng %U https://arxiv.org/abs/1802.03118 %0 Journal Article %J Phys. Rev. Lett. %D 2018 %T Dark state optical lattice with sub-wavelength spatial structure %A Yang Wang %A Sarthak Subhankar %A Przemyslaw Bienias %A Mateusz Lacki %A Tsz-Chun Tsui %A Mikhail A. Baranov %A Alexey V. Gorshkov %A Peter Zoller %A James V. Porto %A Steven L. Rolston %XWe report on the experimental realization of a conservative optical lattice for cold atoms with a subwavelength spatial structure. The potential is based on the nonlinear optical response of three-level atoms in laser-dressed dark states, which is not constrained by the diffraction limit of the light generating the potential. The lattice consists of a one-dimensional array of ultranarrow barriers with widths less than 10 nm, well below the wavelength of the lattice light, physically realizing a Kronig-Penney potential. We study the band structure and dissipation of this lattice and find good agreement with theoretical predictions. Even on resonance, the observed lifetimes of atoms trapped in the lattice are as long as 44 ms, nearly 105times the excited state lifetime, and could be further improved with more laser intensity. The potential is readily generalizable to higher dimensions and different geometries, allowing, for example, nearly perfect box traps, narrow tunnel junctions for atomtronics applications, and dynamically generated lattices with subwavelength spacings.

%B Phys. Rev. Lett. %V 120 %P 083601 %8 2018/02/20 %G eng %U https://link.aps.org/doi/10.1103/PhysRevLett.120.083601 %R 10.1103/PhysRevLett.120.083601 %0 Journal Article %D 2018 %T Demonstration of Bayesian quantum game on an ion trap quantum computer %A Neal Solmeyer %A Norbert M. Linke %A Caroline Figgatt %A Kevin A. Landsman %A Radhakrishnan Balu %A George Siopsis %A Christopher Monroe %XWe demonstrate a Bayesian quantum game on an ion trap quantum computer with five qubits. The players share an entangled pair of qubits and perform rotations on their qubit as the strategy choice. Two five-qubit circuits are sufficient to run all 16 possible strategy choice sets in a game with four possible strategies. The data are then parsed into player types randomly in order to combine them classically into a Bayesian framework. We exhaustively compute the possible strategies of the game so that the experimental data can be used to solve for the Nash equilibria of the game directly. Then we compare the payoff at the Nash equilibria and location of phase-change-like transitions obtained from the experimental data to the theory, and study how it changes as a function of the amount of entanglement.

%G eng %U https://arxiv.org/abs/1802.08116 %0 Journal Article %J Physical Review A %D 2018 %T Diffusion Monte Carlo Versus Adiabatic Computation for Local Hamiltonians %A Jacob Bringewatt %A William Dorland %A Stephen P. Jordan %A Alan Mink %XMost research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real, nonnegative amplitudes. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k-SAT problems, use k-local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n-body interactions. Here we present a new 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

%B Physical Review A %V 97 %P 022323 %8 2018/02/15 %G eng %U https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022323 %N 2 %R 10.1103/PhysRevA.97.022323 %0 Journal Article %J Phys. Rev. A %D 2018 %T Dissipation induced dipole blockade and anti-blockade in driven Rydberg systems %A Jeremy T. Young %A Thomas Boulier %A Eric Magnan %A Elizabeth A. Goldschmidt %A Ryan M. Wilson %A Steven L. Rolston %A James V. Porto %A Alexey V. Gorshkov %XWe study theoretically and experimentally the competing blockade and antiblockade effects induced by spontaneously generated contaminant Rydberg atoms in driven Rydberg systems. These contaminant atoms provide a source of strong dipole-dipole interactions and play a crucial role in the system's behavior. We study this problem theoretically using two different approaches. The first is a cumulant expansion approximation, in which we ignore third-order and higher connected correlations. Using this approach for the case of resonant drive, a many-body blockade radius picture arises, and we find qualitative agreement with previous experimental results. We further predict that as the atomic density is increased, the Rydberg population's dependence on Rabi frequency will transition from quadratic to linear dependence at lower Rabi frequencies. We study this behavior experimentally by observing this crossover at two different atomic densities. We confirm that the larger density system has a smaller crossover Rabi frequency than the smaller density system. The second theoretical approach is a set of phenomenological inhomogeneous rate equations. We compare the results of our rate-equation model to the experimental observations [E. A. Goldschmidt *et al.*, Phys. Rev. Lett. 116, 113001 (2016)] and find that these rate equations provide quantitatively good scaling behavior of the steady-state Rydberg population for both resonant and off-resonant drives.

We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.

%B Phys. Rev. Lett. 121, 043604 %8 2018/07/25 %G eng %U https://arxiv.org/abs/1707.06655 %R https://doi.org/10.1103/PhysRevLett.121.043604 %0 Journal Article %D 2018 %T Distributed Quantum Metrology and the Entangling Power of Linear Networks %A Wenchao Ge %A Kurt Jacobs %A Zachary Eldredge %A Alexey V. Gorshkov %A Michael Foss-Feig %XWe derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.

%8 2018/07/25 %G eng %U https://arxiv.org/abs/1707.06655 %R https://doi.org/10.1103/PhysRevLett.121.043604 %0 Journal Article %D 2018 %T Dynamic suppression of Rayleigh light scattering in dielectric resonators %A Seunghwi Kim %A Jacob M. Taylor %A Gaurav Bahl %XThe ultimate limits of performance for any classical optical system are set by sub-wavelength fluctuations within the host material, that may be frozen-in or even dynamically induced. The most common manifestation of such sub-wavelength disorder is Rayleigh light scattering, which is observed in nearly all wave-guiding technologies today and can lead to both irreversible radiative losses as well as undesirable intermodal coupling. While it has been shown that backscattering from disorder can be suppressed by breaking time-reversal symmetry in magneto-optic and topological insulator materials, common optical dielectrics possess neither of these properties. Here we demonstrate an optomechanical approach for dynamically suppressing Rayleigh backscattering within dielectric resonators. We achieve this by locally breaking time-reversal symmetry in a silica resonator through a Brillouin scattering interaction that is available in all materials. Near-complete suppression of Rayleigh backscattering is experimentally confirmed through three independent measurements -- the reduction of the back-reflections caused by scatterers, the elimination of a commonly seen normal-mode splitting effect, and by measurement of the reduction in intrinsic optical loss. More broadly, our results provide new evidence that it is possible to dynamically suppress Rayleigh backscattering within any optical dielectric medium, for achieving robust light propagation in nanophotonic devices in spite of the presence of scatterers or defects.

%G eng %U https://arxiv.org/abs/1803.02366 %0 Journal Article %J Phys. Rev. Lett. %D 2018 %T Dynamical phase transitions in sampling complexity %A Abhinav Deshpande %A Bill Fefferman %A Minh C. Tran %A Michael Foss-Feig %A Alexey V. Gorshkov %XWe make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time

We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time

Magic state manipulation is a crucial component in the leading approaches to realizing scalable, fault-tolerant, and universal quantum computation. Related to magic state manipulation is the resource theory of magic states, for which one of the goals is to characterize and quantify quantum "magic." In this paper, we introduce the family of thauma measures to quantify the amount of magic in a quantum state, and we exploit this family of measures to address several open questions in the resource theory of magic states. As a first application, we use the min-thauma to bound the regularized relative entropy of magic. As a consequence of this bound, we find that two classes of states with maximal mana, a previously established magic measure, cannot be interconverted in the asymptotic regime at a rate equal to one. This result resolves a basic question in the resource theory of magic states and reveals a fundamental difference between the resource theory of magic states and other resource theories such as entanglement and coherence. As a second application, we establish the hypothesis testing thauma as an efficiently computable benchmark for the one-shot distillable magic, which in turn leads to a variety of bounds on the rate at which magic can be distilled, as well as on the overhead of magic state distillation. Finally, we prove that the max-thauma can outperform mana in benchmarking the efficiency of magic state distillation.

%G eng %U https://arxiv.org/abs/1812.10145 %0 Journal Article %J Optica %D 2018 %T Electro-mechano-optical NMR detection %A Kazuyuki Takeda %A Kentaro Nagasaka %A Atsushi Noguchi %A Rekishu Yamazaki %A Yasunobu Nakamura %A Eiji Iwase %A Jacob M. Taylor %A Koji Usami %XSignal reception of nuclear magnetic resonance (NMR) usually relies on electrical amplification of the electromotive force caused by nuclear induction. Here, we report up-conversion of a radio-frequency NMR signal to an optical regime using a high-stress silicon nitride membrane that interfaces the electrical detection circuit and an optical cavity through the electro-mechanical and the opto-mechanical couplings. This enables optical NMR detection without sacrificing the versatility of the traditional nuclear induction approach. While the signal-to-noise ratio is currently limited by the Brownian motion of the membrane as well as additional technical noise, we find it can exceed that of the conventional electrical schemes by increasing the electro-mechanical coupling strength. The electro-mechano-optical NMR detection presented here can even be combined with the laser cooling technique applied to nuclear spins.

%B Optica %V 5 %P 152-158 %8 2018/02/01 %G eng %U https://www.osapublishing.org/optica/abstract.cfm?uri=optica-5-2-152 %N 2 %R 10.1364/OPTICA.5.000152 %0 Journal Article %D 2018 %T Electro-optomechanical equivalent circuits for quantum transduction %A Emil Zeuthen %A Albert Schliesser %A Jacob M. Taylor %A Anders S. Sørensen %XUsing the techniques of optomechanics, a high-Q mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of classical signals and has the potential of performing quantum state transfer between superconducting circuitry and a traveling optical signal. Such transducers are often operated in a linear regime, where the hybrid system can be described using linear response theory based on the Heisenberg-Langevin equations. While mathematically straightforward to solve, this approach yields little intuition about the dynamics of the hybrid system to aid the optimization of the transducer. As an analysis and design tool for such electro-optomechanical transducers, we introduce an equivalent circuit formalism, where the entire transducer is represented by an electrical circuit. Thereby we integrate the transduction functionality of optomechanical (OM) systems into the toolbox of electrical engineering allowing the use of its well-established design techniques. This unifying impedance description can be applied both for static (DC) and harmonically varying (AC) drive fields, accommodates arbitrary linear circuits, and is not restricted to the resolved-sideband regime. Furthermore, by establishing the quantized input/output formalism for the equivalent circuit, we obtain the scattering matrix for linear transducers using circuit analysis, and thereby have a complete quantum mechanical characterization of the transducer. Hence, this mapping of the entire transducer to the language of electrical engineering both sheds light on how the transducer performs and can at the same time be used to optimize its performance by aiding the design of a suitable electrical circuit.

%8 2018/10/15 %G eng %U https://arxiv.org/abs/1710.10136 %R https://doi.org/10.1103/PhysRevApplied.10.044036 %0 Journal Article %J Phys. Rev. %D 2018 %T Energy-level statistics in strongly disordered systems with power-law hopping %A Paraj Titum %A Victor L. Quito %A Sergey V. Syzranov %XMotivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian ∝1/rα in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focussing on the excitations in disordered electronic systems, we compute the energy-level correlation function R2(ω) in a finite system in the limit of sufficiently strong disorder. At small energy differences the correlations exhibit Wigner-Dyson statistics. In particular, in the limit of very strong disorder the energy-level correlation function is given by R2(ω,V)=A3ωωV for small frequencies ω≪ωV and R2(ω,V)=1−(α−d)A1(ωVω)dα−A2(ωVω)2 for large frequencies ω≫ωV, where ωV∝V−αd is the characteristic matrix element of excitation hopping in a system of volume V, and A1, A2 and A3 are coefficient of order unity which depend on the shape of the system. The energy-level correlation function, which we study, allows for a direct experimental observation, for example, by measuring the correlations of the ac conductance of the system at different frequencies.

%B Phys. Rev. %V B %P 014201 %8 2018/07/16 %G eng %U https://arxiv.org/abs/1803.11178 %N 98 %R https://doi.org/10.1103/PhysRevB.98.014201 %0 Journal Article %J Journal of High Energy Physics %D 2018 %T Entanglement of purification: from spin chains to holography %A Phuc Nguyen %A Trithep Devakul %A Matthew G. Halbasch %A Michael P. Zaletel %A Brian Swingle %XPurification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.

%B Journal of High Energy Physics %P 98 %8 2018/01/22 %G eng %U https://link.springer.com/article/10.1007%2FJHEP01%282018%29098#citeas %R 10.1007/JHEP01(2018)098 %0 Journal Article %D 2018 %T Exact entanglement cost of quantum states and channels under PPT-preserving operations %A Xin Wang %A Mark M. Wilde %XThis paper establishes single-letter formulas for the exact entanglement cost of generating bipartite quantum states and simulating quantum channels under free quantum operations that completely preserve positivity of the partial transpose (PPT). First, we establish that the exact entanglement cost of any bipartite quantum state under PPT-preserving operations is given by a single-letter formula, here called the

Applications of randomness such as private key generation and public randomness beacons require small blocks of certified random bits on demand. Device-independent quantum random number generators can produce such random bits, but existing quantum-proof protocols and loophole-free implementations suffer from high latency, requiring many hours to produce any random bits. We demonstrate device-independent quantum randomness generation from a loophole-free Bell test with a more efficient quantum-proof protocol, obtaining multiple blocks of 512 bits with an average experiment time of less than 5 min per block and with certified error bounded by 2−64≈5.42×10−20.

%G eng %U https://arxiv.org/abs/1812.07786 %0 Journal Article %J Nature %D 2018 %T Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals %A Peter Bierhorst %A Emanuel Knill %A Scott Glancy %A Yanbao Zhang %A Alan Mink %A Stephen Jordan %A Andrea Rommal %A Yi-Kai Liu %A Bradley Christensen %A Sae Woo Nam %A Martin J. Stevens %A Lynden K. Shalm %XFrom dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challenge with random number generators is that it is hard to ensure that their outputs are unpredictable. For a random number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model describing the underlying physics is required to assert unpredictability. Such a model must make a number of assumptions that may not be valid, thereby compromising the integrity of the device. However, it is possible to exploit the phenomenon of quantum nonlocality with a loophole-free Bell test to build a random number generator that can produce output that is unpredictable to any adversary limited only by general physical principles. With recent technological developments, it is now possible to carry out such a loophole-free Bell test. Here we present certified randomness obtained from a photonic Bell experiment and extract 1024 random bits uniform to within 10−12. These random bits could not have been predicted within any physical theory that prohibits superluminal signaling and allows one to make independent measurement choices. To certify and quantify the randomness, we describe a new protocol that is optimized for apparatuses characterized by a low per-trial violation of Bell inequalities. We thus enlisted an experimental result that fundamentally challenges the notion of determinism to build a system that can increase trust in random sources. In the future, random number generators based on loophole-free Bell tests may play a role in increasing the security and trust of our cryptographic systems and infrastructure.

%B Nature %V 556 %P 223-226 %8 2018/04/11 %G eng %U https://arxiv.org/abs/1803.06219 %R https://doi.org/10.1038/s41586-018-0019-0 %0 Journal Article %J Phys. Rev. A 98, 012332 (2018) %D 2018 %T Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory %A Moosavian, Ali Hamed %A Stephen Jordan %XIn quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum Field Theory (QFT) on a quantum computer, which is based on the matrix product state ansatz. We apply this to the massive Gross-Neveu model in one spatial dimension to illustrate the algorithm, but we believe the same algorithm with slight modifications can be used to simulate any one-dimensional massive Fermionic QFT. In the case where the number of particle species is one, our algorithm can prepare particle states using O(ε−3.23…) gates, which is much faster than previous known results, namely O(ε−8−o(1)). Furthermore, unlike previous methods which were based on adiabatic state preparation, the method given here should be able to simulate quantum phases unconnected to the free theory.

%B Phys. Rev. A 98, 012332 (2018) %V A %P 012332 %8 2018/05/04 %G eng %U https://arxiv.org/abs/1711.04006 %N 98 %R https://doi.org/10.1103/PhysRevA.98.012332 %0 Journal Article %D 2018 %T Faster quantum simulation by randomization %A Andrew M. Childs %A Aaron Ostrander %A Yuan Su %XProduct formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and surprisingly efficient. We show that by simply randomizing how the summands are ordered, one can prove stronger bounds on the quality of approximation and thereby give more efficient simulations. Indeed, we show that these bounds can be asymptotically better than previous bounds that exploit commutation between the summands, despite using much less information about the structure of the Hamiltonian. Numerical evidence suggests that our randomized algorithm may be advantageous even for near-term quantum simulation.

%8 2018/05/22 %G eng %U https://arxiv.org/abs/1805.08385 %0 Journal Article %J Science Advances %D 2018 %T Fractal Universality in Near-Threshold Magnetic Lanthanide Dimers %A Constantinos Makrides %A Ming Li %A Eite Tiesinga %A Svetlana Kotochigova %XErgodic quantum systems are often quite alike, whereas nonergodic, fractal systems are unique and display characteristic properties. We explore one of these fractal systems, weakly bound dysprosium lanthanide molecules, in an external magnetic field. As recently shown, colliding ultracold magnetic dysprosium atoms display a soft chaotic behavior with a small degree of disorder. We broaden this classification by investigating the generalized inverse participation ratio and fractal dimensions for large sets of molecular wave functions. Our exact close-coupling simulations reveal a dynamic phase transition from partially localized states to totally delocalized states and universality in its distribution by increasing the magnetic field strength to only a hundred Gauss (or 10 mT). Finally, we prove the existence of nonergodic delocalized phase in the system and explain the violation of ergodicity by strong coupling between near-threshold molecular states and the nearby continuum.

%B Science Advances %V 4 %P eaap8308 %8 2018/02/16 %G eng %U https://arxiv.org/abs/1802.09586 %N 2 %R https://doi.org/10.1126/sciadv.aap8308 %0 Journal Article %D 2018 %T Fractional quantum Hall phases of bosons with tunable interactions: From the Laughlin liquid to a fractional Wigner crystal %A Tobias Graß %A Przemyslaw Bienias %A Michael J. Gullans %A Rex Lundgren %A Joseph Maciejko %A Alexey V. Gorshkov %XHighly tunable platforms for realizing topological phases of matter are emerging from atomic and photonic systems, and offer the prospect of designing interactions between particles. The shape of the potential, besides playing an important role in the competition between different fractional quantum Hall phases, can also trigger the transition to symmetry-broken phases, or even to phases where topological and symmetry-breaking order coexist. Here, we explore the phase diagram of an interacting bosonic model in the lowest Landau level at half-filling as two-body interactions are tuned. Apart from the well-known Laughlin liquid, Wigner crystal phase, stripe, and bubble phases, we also find evidence of a phase that exhibits crystalline order at fractional filling per crystal site. The Laughlin liquid transits into this phase when pairs of bosons strongly repel each other at relative angular momentum 4ℏ. We show that such interactions can be achieved by dressing ground-state cold atoms with multiple different-parity Rydberg states.

%G eng %U https://arxiv.org/abs/1809.04493 %0 Journal Article %J Physical Review A %D 2018 %T Geometry of the quantum set of correlations %A Koon Tong Goh %A Jedrzej Kaniewski %A Elie Wolfe %A Tamás Vértesi %A Xingyao Wu %A Yu Cai %A Yeong-Cherng Liang %A Valerio Scarani %XIt is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not have good intuition about what the quantum set actually looks like. In this paper we study the geometry of the quantum set using standard tools from convex geometry. We find explicit examples of rather counter-intuitive features in the simplest non-trivial Bell scenario (two parties, two inputs and two outputs) and illustrate them using 2-dimensional slice plots. We also show that even more complex features appear in Bell scenarios with more inputs or more parties. Finally, we discuss the limitations that the geometry of the quantum set imposes on the task of self-testing.

%B Physical Review A %V 97 %P 022104 %8 2018/02/07 %G eng %U https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022104 %N 2 %R 10.1103/PhysRevA.97.022104 %0 Journal Article %D 2018 %T High Purity Single Photons Entangled with an Atomic Memory %A Clayton Crocker %A Martin Lichtman %A Ksenia Sosnova %A Allison Carter %A Sophia Scarano %A Christopher Monroe %XTrapped atomic ions are an ideal candidate for quantum network nodes, with long-lived identical qubit memories that can be locally entangled through their Coulomb interaction and remotely entangled through photonic channels. The integrity of this photonic interface is generally reliant on purity of single photons produced by the quantum memory. Here we demonstrate a single-photon source for quantum networking based on a trapped 138Ba+ ion with a single photon purity of g2(0)=(8.1±2.3)×10−5 without background subtraction. We further optimize the tradeoff between the photonic generation rate and the memory-photon entanglement fidelity for the case of polarization photonic qubits by tailoring the spatial mode of the collected light.

%G eng %U https://arxiv.org/abs/1812.01749 %0 Journal Article %J Physical Review B %D 2018 %T High-fidelity quantum gates in Si/SiGe double quantum dots %A Maximilian Russ %A D. M. Zajac %A A. J. Sigillito %A F. Borjans %A J. M. Taylor %A J. R. Petta %A Guido Burkard %XMotivated by recent experiments of Zajac *et al.* [Science 359, 439 (2018)], we theoretically describe high-fidelity two-qubit gates using the exchange interaction between the spins in neighboring quantum dots subject to a magnetic field gradient. We use a combination of analytical calculations and numerical simulations to provide the optimal pulse sequences and parameter settings for the gate operation. We present a synchronization method which avoids detrimental spin flips during the gate operation and provide details about phase mismatches accumulated during the two-qubit gates which occur due to residual exchange interaction, nonadiabatic pulses, and off-resonant driving. By adjusting the gate times, synchronizing the resonant and off-resonant transitions, and compensating these phase mismatches by phase control, the overall gate fidelity can be increased significantly.

We study the holographic complexity of Einstein-Maxwell-Dilaton gravity using the recently proposed "complexity = volume" and "complexity = action" dualities. The model we consider has a ground state that is represented in the bulk via a so-called hyperscaling violating geometry. We calculate the action growth of the Wheeler-DeWitt patch of the corresponding black hole solution at non-zero temperature and find that, in the presence of violations of hyperscaling, there is a parametric enhancement of the action growth rate. We partially match this behavior to simple tensor network models which can capture aspects of hyperscaling violation. We also exhibit the switchback effect in complexity growth using shockwave geometries and comment on a subtlety of our action calculations when the metric is discontinuous at a null surface.

%B J. High Energ. Phys. %V 106 %8 2018 %G eng %U https://arxiv.org/abs/1712.09826 %R https://doi.org/10.1007/JHEP09(2018)106 %0 Journal Article %D 2018 %T Implicit regularization and solution uniqueness in over-parameterized matrix sensing %A Anastasios Kyrillidis %A Amir Kalev %XWe consider whether algorithmic choices in over-parameterized linear matrix factorization introduce implicit regularization. We focus on noiseless matrix sensing over rank-r positive semi-definite (PSD) matrices in Rn×n, with a sensing mechanism that satisfies the restricted isometry property (RIP). The algorithm we study is that of \emph{factored gradient descent}, where we model the low-rankness and PSD constraints with the factorization UU⊤, where U∈Rn×r. Surprisingly, recent work argues that the choice of r≤n is not pivotal: even setting U∈Rn×n is sufficient for factored gradient descent to find the rank-r solution, which suggests that operating over the factors leads to an implicit regularization. In this note, we provide a different perspective. We show that, in the noiseless case, under certain conditions, the PSD constraint by itself is sufficient to lead to a unique rank-r matrix recovery, without implicit or explicit low-rank regularization. \emph{I.e.}, under assumptions, the set of PSD matrices, that are consistent with the observed data, is a singleton, irrespective of the algorithm used.

%G eng %U https://arxiv.org/abs/1806.02046 %0 Journal Article %J forthcoming in Studies in History and Philosophy of Modern Physics %D 2018 %T In Defense of a "Single-World" Interpretation of Quantum Mechanics %A Jeffrey Bub %XIn a recent result, Frauchiger and Renner argue that if quantum theory accurately describes complex systems like observers who perform measurements, then "we are forced to give up the view that there is one single reality." Following a review of the Frauchiger-Renner argument, I argue that quantum mechanics should be understood probabilistically, as a new sort of non-Boolean probability theory, rather than representationally, as a theory about the elementary constituents of the physical world and how these elements evolve dynamically over time. I show that this way of understanding quantum mechanics is not in conflict with a consistent "single-world" interpretation of the theory.

%B forthcoming in Studies in History and Philosophy of Modern Physics %P 15 %G eng %U https://arxiv.org/abs/1804.03267 %0 Journal Article %D 2018 %T Information-Theoretic Privacy For Distributed Average Consensus: Bounded Integral Inputs %A Nirupam Gupta %A Jonathan Katz %A Nikhil Chopra %XWe propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents' inputs against colluding passive adversarial agents, as long as the set of colluding passive adversarial agents is not a vertex cut in the underlying communication network. This implies that a network with (t+1)-connectivity guarantees information-theoretic privacy of honest agents' inputs against any t colluding agents. The proposed protocol is formed by composing a distributed privacy mechanism we provide with any (non-private) distributed average consensus algorithm. The agent' inputs are bounded integers, where the bounds are apriori known to all the agents.

%8 03/28/2019 %G eng %U https://arxiv.org/abs/1809.01794 %0 Journal Article %D 2018 %T Information-Theoretic Privacy in Distributed Average Consensus %A Nirupam Gupta %A Jonathan Katz %A Nikhil Chopra %XWe propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents' inputs against colluding semi-honest (passively adversarial) agents, as long as the set of colluding semi-honest agents is not a vertex cut in the underlying communication network. This implies that a network with

If a measurement is made on one half of a bipartite system then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explanation — that is, if shared randomness cannot produce these reduced states for all possible measurements — the bipartite state is said to be steerable. Determining which states are steerable is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for T-states (that is, those with maximally mixed marginals) under projective measurements. In the current work we introduce the concept of keyring models — a special class of local hidden state model. When the measurements made correspond to real projectors, these allow us to study steerability beyond T-states. Using keyring models, we completely solve the steering problem for real projective measurements when the state arises from mixing a pure two-qubit state with uniform noise. We also give a partial solution in the case when the uniform noise is replaced by independent depolarizing channels. Our results imply that Werner states, which are a special case of the previous states, are unsteerable under real projective measurements if and only if their efficiency is at most 2/π.

%B Journal of Mathematical Physics %V 59 %P 022103 %8 2018/01/02 %G eng %U http://aip.scitation.org/doi/full/10.1063/1.5006199 %R 10.1063/1.5006199 %0 Journal Article %J Phys. Rev. A %D 2018 %T Local randomness: Examples and application %A Honghao Fu %A Carl Miller %XWhen two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed [C. Miller and Y. Shi, Quantum Inf. Computat. 17, 0595 (2017)] that such scores also imply the existence of local randomness—that is, randomness known to one player but not to the other. This has potential implications for cryptographic tasks between two cooperating but mistrustful players. In the current paper we bring this notion toward practical realization, by offering near-optimal bounds on local randomness for the CHSH game, and also proving the security of a cryptographic application of local randomness (single-bit certified deletion).

%B Phys. Rev. A %P 032324 %8 03/2018 %G eng %U https://arxiv.org/abs/1708.04338 %N 97 %R https://doi.org/10.1103/PhysRevA.97.032324 %0 Journal Article %D 2018 %T Locality, Quantum Fluctuations, and Scrambling %A Shenglong Xu %A Brian Swingle %XThermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large N models exhibiting exponential growth of OTOCs and a sharp chaos wavefront and other random circuit models showing a diffusively broadened wavefront. In this paper we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large N limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wavefront. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a cross-over to a diffusively broadened wavefront. At small N we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively-broadened wavefront.

%G eng %U https://arxiv.org/abs/1805.05376 %0 Journal Article %J J. Phys. B: At. Mol. Opt. Phys. %D 2018 %T Machine learning assisted readout of trapped-ion qubits %A Alireza Seif %A Kevin A. Landsman %A Norbert M. Linke %A Caroline Figgatt %A C. Monroe %A Mohammad Hafezi %XWe reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30\% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms.

%B J. Phys. B: At. Mol. Opt. Phys. %V 51 %8 2018/05/01 %G eng %U https://arxiv.org/abs/1804.07718 %& 174006 %R https://doi.org/10.1088/1361-6455/aad62b %0 Journal Article %D 2018 %T Mathematical methods for resource-based type theories %A Aarthi Sundaram %A Brad Lackey %XWith the wide range of quantum programming languages on offer now, efficient program verification and type checking for these languages presents a challenge -- especially when classical debugging techniques may affect the states in a quantum program. In this work, we make progress towards a program verification approach using the formalism of operational quantum mechanics and resource theories. We present a logical framework that captures two mathematical approaches to resource theory based on monoids (algebraic) and monoidal categories (categorical). We develop the syntax of this framework as an intuitionistic sequent calculus, and prove soundness and completeness of an algebraic and categorical semantics that recover these approaches. We also provide a cut-elimination theorem, normal form, and analogue of Lambek's lifting theorem for polynomial systems over the logics. Using these approaches along with the Curry-Howard-Lambek correspondence for programs, proofs and categories, this work lays the mathematical groundwork for a type checker for some resource theory based frameworks, with the possibility of extending it other quantum programming languages.

%G eng %U https://arxiv.org/abs/1812.08726 %0 Journal Article %J New Journal of Physics %D 2018 %T Measurement Contextuality and Planck's Constant %A Lucas Kocia %A Peter Love %XContextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, ℏ, can also be used to characterize the classical-quantum divide by expanding quantities of interest in powers of ℏ---all orders higher than ℏ0 can be interpreted as quantum corrections to the order ℏ0 term. We show that contextual measurements in finite-dimensional systems have formulations within the Wigner-Weyl-Moyal (WWM) formalism that require higher than order ℏ0 terms to be included in order to violate the classical bounds on their expectation values. As a result, we show that contextuality as a resource is equivalent to orders of ℏ as a resource within the WWM formalism. This explains why qubits can only exhibit state-independent contextuality under Pauli observables as in the Peres-Mermin square while odd-dimensional qudits can also exhibit state-dependent contextuality. In particular, we find that qubit Pauli observables lack an order ℏ0 contribution in their Weyl symbol and so exhibit contextuality regardless of the state being measured. On the other hand, odd-dimensional qudit observables generally possess non-zero order ℏ0 terms, and higher, in their WWM formulation, and so exhibit contextuality depending on the state measured: odd-dimensional qudit states that exhibit measurement contextuality have an order ℏ1 contribution that allows for the violation of classical bounds while states that do not exhibit measurement contextuality have insufficiently large order ℏ1 contributions.

%B New Journal of Physics %V 20 %P 073020 %8 2018/07/12 %G eng %U https://arxiv.org/abs/1711.08066 %N 7 %R https://doi.org/10.1088/1367-2630/aacef2 %0 Journal Article %D 2018 %T More is Less: Perfectly Secure Oblivious Algorithms in the Multi-Server Setting %A Hubert Chan %A Jonathan Katz %A Kartik Nayak %A Antigoni Polychroniadou %A Elaine Shi %XThe problem of Oblivious RAM (ORAM) has traditionally been studied in a single-server setting, but more recently the multi-server setting has also been considered. Yet it is still unclear whether the multi-server setting has any inherent advantages, e.g., whether the multi-server setting can be used to achieve stronger security goals or provably better efficiency than is possible in the single-server case. In this work, we construct a perfectly secure 3-server ORAM scheme that outperforms the best known single-server scheme by a logarithmic factor. In the process, we also show, for the first time, that there exist specific algorithms for which multiple servers can overcome known lower bounds in the single-server setting.

%G eng %U https://arxiv.org/abs/1809.00825 %0 Journal Article %D 2018 %T Morphisms in categories of nonlocal games %A Brad Lackey %A Nishant Rodrigues %XSynchronous correlations provide a class of nonlocal games that behave like functions between finite sets. In this work we examine categories whose morphisms are games with synchronous classical, quantum, or general nonsignaling correlations. In particular, we characterize when morphisms in these categories are monic, epic, sections, or retractions.

%G eng %U https://arxiv.org/abs/1810.10074 %0 Journal Article %D 2018 %T Multiparty quantum data hiding with enhanced security and remote deletion %A Xingyao Wu %A Jianxin Chen %XOne of the applications of quantum technology is to use quantum states and measurements to communicate which offers more reliable security promises. Quantum data hiding, which gives the source party the ability of sharing data among multiple receivers and revealing it at a later time depending on his/her will, is one of the promising information sharing schemes which may address practical security issues. In this work, we propose a novel quantum data hiding protocol. By concatenating different subprotocols which apply to rather symmetric hiding scenarios, we cover a variety of more general hiding scenarios. We provide the general requirements for constructing such protocols and give explicit examples of encoding states for five parties. We also proved the security of the protocol in sense that the achievable information by unauthorized operations asymptotically goes to zero. In addition, due to the capability of the sender to manipulate his/her subsystem, the sender is able to abort the protocol remotely at any time before he/she reveals the information.

%P 5 %G eng %U https://arxiv.org/abs/1804.01982 %0 Journal Article %J High Energ. Phys. %D 2018 %T On the need for soft dressing %A Daniel Carney %A Laurent Chaurette %A Dominik Neuenfeld %A Gordon Semenoff %XIn order to deal with IR divergences arising in QED or perturbative quantum gravity scattering processes, one can either calculate inclusive quantities or use dressed asymptotic states. We consider incoming superpositions of momentum eigenstates and show that in calculations of cross-sections these two approaches yield different answers: in the inclusive formalism no interference occurs for incoming finite superpositions and wavepackets do not scatter at all, while the dressed formalism yields the expected interference terms. This suggests that rather than Fock space states, one should use Faddeev-Kulish-type dressed states to correctly describe physical processes involving incoming superpositions. We interpret this in terms of selection rules due to large U(1) gauge symmetries and BMS supertranslations.

%B High Energ. Phys. %V 121 %8 2018 %G eng %0 Journal Article %D 2018 %T On non-adaptive quantum chosen-ciphertext attacks and Learning with Errors %A Gorjan Alagic %A Stacey Jeffery %A Maris Ozols %A Alexander Poremba %XLarge-scale quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants the adversary quantum oracle access to encryption and decryption, but where the latter is restricted to non-adaptive (i.e., pre-challenge) queries only. We define this model formally using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. Using a bound on quantum random-access codes, we show that the standard PRF- and PRP-based encryption schemes are QCCA1-secure when instantiated with quantum-secure primitives. We then revisit standard IND-CPA-secure Learning with Errors (LWE) encryption and show that leaking just one quantum decryption query (and no other queries or leakage of any kind) allows the adversary to recover the full secret key with constant success probability. In the classical setting, by contrast, recovering the key uses a linear number of decryption queries, and this is optimal. The algorithm at the core of our attack is a (large-modulus version of) the well-known Bernstein-Vazirani algorithm. We emphasize that our results should *not* be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.

%G eng %U https://arxiv.org/abs/1808.09655 %0 Journal Article %D 2018 %T The Non-Disjoint Ontic States of the Grassmann Ontological Model, Transformation Contextuality, and the Single Qubit Stabilizer Subtheory %A Lucas Kocia %A Peter Love %XWe show that it is possible to construct a preparation non-contextual ontological model that does not exhibit "transformation contextuality" for single qubits in the stabilizer subtheory. In particular, we consider the "blowtorch" map and show that it does not exhibit transformation contextuality under the Grassmann Wigner-Weyl-Moyal (WWM) qubit formalism. Furthermore, the transformation in this formalism can be fully expressed at order ℏ0 and so does not qualify as a candidate quantum phenomenon. In particular, we find that the Grassmann WWM formalism at order ℏ0 corresponds to an ontological model governed by an additional set of constraints arising from the relations defining the Grassmann algebra. Due to this additional set of constraints, the allowed probability distributions in this model do not form a single convex set when expressed in terms of disjoint ontic states and so cannot be mapped to models whose states form a single convex set over disjoint ontic states. However, expressing the Grassmann WWM ontological model in terms of non-disjoint ontic states corresponding to the monomials of the Grassmann algebra results in a single convex set. We further show that a recent result by Lillystone et al. that proves a broad class of preparation and measurement non-contextual ontological models must exhibit transformation contextuality lacks the generality to include the ontological model considered here; Lillystone et al.'s result is appropriately limited to ontological models whose states produce a single convex set when expressed in terms of disjoint ontic states. Therefore, we prove that for the qubit stabilizer subtheory to be captured by a preparation, transformation and measurement non-contextual ontological theory, it must be expressed in terms of non-disjoint ontic states, unlike the case for the odd-dimensional single-qudit stabilizer subtheory.

%G eng %U https://arxiv.org/abs/1805.09514 %0 Journal Article %J Nature Communications %D 2018 %T Observation of bound state self-interaction in a nano-eV atom collider %A Ryan Thomas %A Matthew Chilcott %A Eite Tiesinga %A Amita B. Deb %A Niels Kjærgaard %XQuantum mechanical scattering resonances for colliding particles occur when a continuum scattering state couples to a discrete bound state between them. The coupling also causes the bound state to interact with itself via the continuum and leads to a shift in the bound state energy, but, lacking knowledge of the bare bound state energy, measuring this self-energy via the resonance position has remained elusive. Here, we report on the direct observation of self-interaction by using a nano-eV atom collider to track the position of a magnetically-tunable Feshbach resonance through a parameter space spanned by energy and magnetic field. Our system of potassium and rubidium atoms displays a strongly non-monotonic resonance trajectory with an exceptionally large self-interaction energy arising from an interplay between the Feshbach bound state and a different, virtual bound state at a fixed energy near threshold.

%B Nature Communications %V 9 %8 2018/11/20 %G eng %U https://arxiv.org/abs/1807.01174 %N 4895 %R https://doi.org/10.1038/s41467-018-07375-8 %0 Journal Article %J Science %D 2018 %T Observation of three-photon bound states in a quantum nonlinear medium %A Qi-Yu Liang %A Aditya V. Venkatramani %A Sergio H. Cantu %A Travis L. Nicholson %A Michael J. Gullans %A Alexey V. Gorshkov %A Jeff D. Thompson %A Cheng Chin %A Mikhail D. Lukin %A Vladan Vuletic %XBound states of massive particles, such as nuclei, atoms or molecules, are ubiquitous in nature and constitute the bulk of the visible world around us. In contrast, photons typically only weakly influence each other due to their very weak interactions and vanishing mass. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. In particular, photon correlation and conditional phase measurements reveal the distinct features associated with three-photon and two-photon bound states. Such photonic trimers and dimers can be viewed as quantum solitons with shape-preserving wavefunctions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are quantitatively described by an effective field theory (EFT) of Rydberg-induced photon-photon interactions, which demonstrates the presence of a substantial effective three-body force between the photons. These observations pave the way towards the realization, studies, and control of strongly interacting quantum many-body states of light.

%B Science %V 359 %P 783-786 %8 2018/02/16 %G eng %U http://science.sciencemag.org/content/359/6377/783 %N 6377 %R 10.1126/science.aao7293 %0 Journal Article %D 2018 %T Optimal and Secure Measurement Protocols for Quantum Sensor Networks %A Zachary Eldredge %A Michael Foss-Feig %A Steven L. Rolston %A Alexey V. Gorshkov %XStudies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting where the quantity to be measured is a linear function of parameters coupled to each qubit individually. We first generalize the Heisenberg limit to the measurement of non-local observables in a quantum network, deriving a bound based on the multi-parameter quantum Fisher information. We then propose a protocol that can make use of GHZ states or spin-squeezed states, and show that in the case of GHZ states the procedure is optimal, i.e., it saturates our bound.

%8 2018/03/23 %G eng %U http://arxiv.org/abs/1607.04646 %R https://doi.org/10.1103/PhysRevA.97.042337 %0 Journal Article %J Phys. Rev. Lett. %D 2018 %T Optimal Pure-State Qubit Tomography via Sequential Weak Measurements %A Ezad Shojaee %A Christopher S. Jackson %A Carlos A. Riofrio %A Amir Kalev %A Ivan H. Deutsch %XThe spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space probabilities. We prove that this POVM is achieved by collectively measuring the spin projection of an ensemble of qubits weakly and isotropically. We apply this in the context of optimal tomography of pure qubits. We show numerically that through a sequence of weak measurements of random directions of the collective spin component, sampled discretely or in a continuous measurement with random controls, one can approach the optimal bound.

%B Phys. Rev. Lett. %V 121 %G eng %U https://arxiv.org/abs/1805.01012 %N 130404 %R https://doi.org/10.1103/PhysRevLett.121.130404 %0 Journal Article %J New Journal of Physics %D 2018 %T Optimization of photon storage fidelity in ordered atomic arrays %A M. T. Manzoni %A M. Moreno-Cardoner %A A. Asenjo-Garcia %A J. V. Porto %A Alexey V. Gorshkov %A D. E. Chang %XA major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell-Bloch equations. The validity of this model can break down, however, in systems such as dense, ordered atomic arrays, where strong interference in emission can give rise to phenomena such as subradiance and "selective" radiance. Here, we develop a general formalism that finds the maximum storage efficiency for a collection of atoms with discrete, known positions, and a given spatial mode in which an optical field is sent. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number Na like ∼(logNa)2/N2a, and that, remarkably, an array of just 4×4 atoms in principle allows for an efficiency comparable to a disordered ensemble with optical depth of around 600.

%B New Journal of Physics %V 20 %8 2018/08/31 %G eng %U https://arxiv.org/abs/1710.06312 %N 083048 %R https://doi.org/10.1088/1367-2630/aadb74 %0 Journal Article %J Phys. Rev. A 97, 033850 %D 2018 %T Optomechanical approach to controlling the temperature and chemical potential of light %A Chiao-Hsuan Wang %A Jacob M. Taylor %XMassless particles, including photons, are not conserved even at low energies and thus have no chemical potential. However, in driven systems, near equilibrium dynamics can lead to equilibration of photons with a finite number, describable using an effective chemical potential. Here we build upon this general concept with an implementation appropriate for a nonlinear photon-based quantum simulator. We consider how laser cooling of a well-isolated mechanical mode can provide an effective low-frequency bath for the quantum simulator system. We show that the use of auxiliary photon modes, coupled by the mechanical system, enables control of both the chemical potential, by drive frequency, and temperature, by drive amplitude, of the resulting photonic quantum simulator's grand canonical ensemble.

%B Phys. Rev. A 97, 033850 %8 2018/05/18 %G eng %U https://arxiv.org/abs/1706.00789 %R https://doi.org/10.1103/PhysRevA.97.033850 %0 Journal Article %D 2018 %T Orbital quantum magnetism in spin dynamics of strongly interacting magnetic lanthanide atoms %A Ming Li %A Eite Tiesinga %A Svetlana Kotochigova %XLaser cooled lanthanide atoms are ideal candidates with which to study strong and unconventional quantum magnetism with exotic phases. Here, we use state-of-the-art closed-coupling simulations to model quantum magnetism for pairs of ultracold spin-6 erbium lanthanide atoms placed in a deep optical lattice. In contrast to the widely used single-channel Hubbard model description of atoms and molecules in an optical lattice, we focus on the single-site multi-channel spin evolution due to spin-dependent contact, anisotropic van der Waals, and dipolar forces. This has allowed us to identify the leading mechanism, orbital anisotropy, that governs molecular spin dynamics among erbium atoms. The large magnetic moment and combined orbital angular momentum of the 4f-shell electrons are responsible for these strong anisotropic interactions and unconventional quantum magnetism. Multi-channel simulations of magnetic Cr atoms under similar trapping conditions show that their spin-evolution is controlled by spin-dependent contact interactions that are distinct in nature from the orbital anisotropy in Er. The role of an external magnetic field and the aspect ratio of the lattice site on spin dynamics is also investigated.

%G eng %U https://arxiv.org/abs/1804.10102 %0 Journal Article %D 2018 %T Parallel Entangling Operations on a Universal Ion Trap Quantum Computer %A C. Figgatt %A A. Ostrander %A N. M. Linke %A K. A. Landsman %A D. Zhu %A D. Maslov %A C. Monroe %XThe circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear efficiency gains in numerous quantum circuits as well as for entire algorithms such as Shor's factoring algorithm and quantum simulations. In cases such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time. More importantly, quantum gate parallelism is essential for the practical fault-tolerant error correction of qubits that suffer from idle errors. The implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions or cavity-coupled superconducting transmons. Here, we present the first experimental results for parallel 2-qubit entangling gates in an array of fully-connected trapped ion qubits. We demonstrate an application of this capability by performing a 1-bit full addition operation on a quantum computer using a depth-4 quantum circuit. These results exploit the power of highly connected qubit systems through classical control techniques, and provide an advance toward speeding up quantum circuits and achieving fault tolerance with trapped ion quantum computers.

%G eng %U https://arxiv.org/abs/1810.11948 %0 Journal Article %J IEEE Transactions on Information Theory %D 2018 %T Phase Retrieval Without Small-Ball Probability Assumptions %A Felix Krahmer %A Yi-Kai Liu %XIn the context of the phase retrieval problem, it is known that certain natural classes of measurements, such as Fourier measurements and random Bernoulli measurements, do not lead to the unique reconstruction of all possible signals, even in combination with certain practically feasible random masks. To avoid this difficulty, the analysis is often restricted to measurement ensembles (or masks) that satisfy a small-ball probability condition, in order to ensure that the reconstruction is unique. This paper shows a complementary result: for random Bernoulli measurements, there is still a large class of signals that can be reconstructed uniquely, namely, those signals that are non-peaky. In fact, this result is much more general: it holds for random measurements sampled from any subgaussian distribution 2), without any small-ball conditions. This is demonstrated in two ways: 1) a proof of stability and uniqueness and 2) a uniform recovery guarantee for the PhaseLift algorithm. In all of these cases, the number of measurements m approaches the information-theoretic lower bound. Finally, for random Bernoulli measurements with erasures, it is shown that PhaseLift achieves uniform recovery of all signals (including peaky ones).

%B IEEE Transactions on Information Theory %V 64 %P 485-500 %8 2018/01/01 %G eng %U http://ieeexplore.ieee.org/document/8052535/ %N 1 %R 10.1109/TIT.2017.2757520 %0 Journal Article %D 2018 %T Photon propagation through dissipative Rydberg media at large input rates %A Przemyslaw Bienias %A James Douglas %A Asaf Paris-Mandoki %A Paraj Titum %A Ivan Mirgorodskiy %A Christoph Tresp %A Emil Zeuthen %A Michael J. Gullans %A Marco Manzoni %A Sebastian Hofferberth %A Darrick Chang %A Alexey V. Gorshkov %XWe study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency (EIT). Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions between single photons. The regime of high incoming photon flux constitutes a challenging many-body dissipative problem. We experimentally study in detail for the first time the pulse shapes and the second-order correlation function of the outgoing field and compare our data with simulations based on two novel theoretical approaches well-suited to treat this many-photon limit. At low incoming flux, we report good agreement between both theories and the experiment. For higher input flux, the intensity of the outgoing light is lower than that obtained from theoretical predictions. We explain this discrepancy using a simple phenomenological model taking into account pollutants, which are nearly-stationary Rydberg excitations coming from the reabsorption of scattered probe photons. At high incoming photon rates, the blockade physics results in unconventional shapes of measured correlation functions.

%G eng %U https://arxiv.org/abs/1807.07586 %0 Journal Article %D 2018 %T Photon Subtraction by Many-Body Decoherence %A Callum R. Murray %A Ivan Mirgorodskiy %A Christoph Tresp %A Christoph Braun %A Asaf Paris-Mandoki %A Alexey V. Gorshkov %A Sebastian Hofferberth %A Thomas Pohl %XWe present an experimental and theoretical investigation of the scattering-induced decoherence of multiple photons stored in a strongly interacting atomic ensemble. We derive an exact solution to this many-body problem, allowing for a rigorous understanding of the underlying dissipative quantum dynamics. Combined with our experiments, this analysis demonstrates a correlated coherence-protection process, in which the induced decoherence of one photon can preserve the spatial coherence of all others. We discuss how this effect can be used to manipulate light at the quantum level, providing a robust mechanism for single-photon subtraction, and experimentally demonstrate this capability.

%8 2018/03/13 %G eng %U https://arxiv.org/abs/1710.10047 %R https://doi.org/10.1103/PhysRevLett.120.113601 %0 Journal Article %J Phys. Rev. A 98, 013834 %D 2018 %T Photon thermalization via laser cooling of atoms %A Chiao-Hsuan Wang %A M. J. Gullans %A J. V. Porto %A William D. Phillips %A Jacob M. Taylor %XLaser cooling of atomic motion enables a wide variety of technological and scientific explorations using cold atoms. Here we focus on the effect of laser cooling on the photons instead of on the atoms. Specifically, we show that non-interacting photons can thermalize with the atoms to a grand canonical ensemble with a non-zero chemical potential. This thermalization is accomplished via scattering of light between different optical modes, mediated by the laser cooling process. While optically thin modes lead to traditional laser cooling of the atoms, the dynamics of multiple scattering in optically thick modes has been more challenging to describe. We find that in an appropriate set of limits, multiple scattering leads to thermalization of the light with the atomic motion in a manner that approximately conserves total photon number between the laser beams and optically thick modes. In this regime, the subsystem corresponding to the thermalized modes is describable by a grand canonical ensemble with a chemical potential set by the energy of a single laser photon. We consider realization of this regime using two-level atoms in Doppler cooling, and find physically realistic conditions for rare earth atoms. With the addition of photon-photon interactions, this system could provide a new platform for exploring many-body physics.

%B Phys. Rev. A 98, 013834 %8 2018 %G eng %U https://arxiv.org/abs/1712.08643 %R https://doi.org/10.1103/PhysRevA.98.013834 %0 Journal Article %D 2018 %T Practitioner's guide to social network analysis: Examining physics anxiety in an active-learning setting %A Remy Dou %A Justyna P. Zwolak %XThe application of social network analysis (SNA) has recently grown prevalent in science, technology, engineering, and mathematics education research. Research on classroom networks has led to greater understandings of student persistence in physics majors, changes in their career-related beliefs (e.g., physics interest), and their academic success. In this paper, we aim to provide a practitioner's guide to carrying out research using SNA, including how to develop data collection instruments, set up protocols for gathering data, as well as identify network methodologies relevant to a wide range of research questions beyond what one might find in a typical primer. We illustrate these techniques using student anxiety data from active-learning physics classrooms. We explore the relationship between students' physics anxiety and the social networks they participate in throughout the course of a semester. We find that students' with greater numbers of outgoing interactions are more likely to experience negative anxiety shifts even while we control for {\it pre} anxiety, gender, and final course grade. We also explore the evolution of student networks and find that the second half of the semester is a critical period for participating in interactions associated with decreased physics anxiety. Our study further supports the benefits of dynamic group formation strategies that give students an opportunity to interact with as many peers as possible throughout a semester. To complement our guide to SNA in education research, we also provide a set of tools for letting other researchers use this approach in their work -- the {\it SNA toolbox} -- that can be accessed on GitHub.

%G eng %U https://arxiv.org/abs/1809.00337 %0 Journal Article %J Physical Review B %D 2018 %T Probing electron-phonon interactions in the charge-photon dynamics of cavity-coupled double quantum dots %A M. J. Gullans %A J. M. Taylor %A J. R. Petta %XElectron-phonon coupling is known to play an important role in the charge dynamics of semiconductor quantum dots. Here we explore its role in the combined charge-photon dynamics of cavity-coupled double quantum dots. Previous work on these systems has shown that strong electron-phonon coupling leads to a large contribution to photoemission and gain from phonon-assisted emission and absorption processes. We compare the effects of this phonon sideband in three commonly investigated gate-defined quantum dot material systems: InAs nanowires and GaAs and Si two-dimensional electron gases (2DEGs). We compare our theory with existing experimental data from cavity-coupled InAs nanowire and GaAs 2DEG double quantum dots and find quantitative agreement only when the phonon sideband and photoemission processes during lead tunneling are taken into account. Finally, we show that the phonon sideband also leads to a sizable renormalization of the cavity frequency, which allows for direct spectroscopic probes of the electron-phonon coupling in these systems.

%B Physical Review B %V 97 %P 035305 %8 2018/01/16 %G eng %U https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.035305 %N 3 %R 10.1103/PhysRevB.97.035305 %0 Journal Article %D 2018 %T Probing ground-state phase transitions through quench dynamics %A Paraj Titum %A Joseph T. Iosue %A James R. Garrison %A Alexey V. Gorshkov %A Zhe-Xuan Gong %XThe study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a non-analytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal time scales. Therefore, our method can be used to approximately locate the quantum critical point. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.

%G eng %U https://arxiv.org/abs/1809.06377 %0 Journal Article %D 2018 %T Product Spectrum Ansatz and the Simplicity of Thermal States %A John Martyn %A Brian Swingle %XCalculating the physical properties of quantum thermal states is a difficult problem for classical computers, rendering it intractable for most quantum many-body systems. A quantum computer, by contrast, would make many of these calculations feasible in principle, but it is still non-trivial to prepare a given thermal state or sample from it. It is also not known how to prepare special simple purifications of thermal states known as thermofield doubles, which play an important role in quantum many-body physics and quantum gravity. To address this problem, we propose a variational scheme to prepare approximate thermal states on a quantum computer by applying a series of two-qubit gates to a product mixed state. We apply our method to a non-integrable region of the mixed field Ising chain and the Sachdev-Ye-Kitaev model. We also demonstrate how our method can be easily extended to large systems governed by local Hamiltonians and the preparation of thermofield double states. By comparing our results with exact solutions, we find that our construction enables the efficient preparation of approximate thermal states on quantum devices. Our results can be interpreted as implying that the details of the many-body energy spectrum are not needed to capture simple thermal observables.

%G eng %U https://arxiv.org/abs/1812.01015 %0 Journal Article %J In: Shacham H., Boldyreva A. (eds) Advances in Cryptology – CRYPTO 2018. CRYPTO 2018. Lecture Notes in Computer Science. %D 2018 %T Pseudorandom States, Non-Cloning Theorems and Quantum Money %A Zhengfeng Ji %A Yi-Kai Liu %A Fang Song %XWe propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom states. The non-cloning theorem plays a central role in our study—it motivates the proper definition and characterizes one of the important properties of pseudorandom quantum states. Namely, there is no efficient quantum algorithm that can create more copies of the state from a given number of pseudorandom states. As the main application, we prove that any family of pseudorandom states naturally gives rise to a private-key quantum money scheme.

%B In: Shacham H., Boldyreva A. (eds) Advances in Cryptology – CRYPTO 2018. CRYPTO 2018. Lecture Notes in Computer Science. %V 10993 %8 2017/11/01 %G eng %U https://arxiv.org/abs/1711.00385 %R https://doi.org/10.1007/978-3-319-96878-0_5 %0 Journal Article %J PLOS ONE %D 2018 %T QFlow lite dataset: A machine-learning approach to the charge states in quantum dot experiments %A Justyna P. Zwolak %A Sandesh S. Kalantre %A Xingyao Wu %A Stephen Ragole %A Jacob M. Taylor %XOver the past decade, machine learning techniques have revolutionized how research is done, from designing new materials and predicting their properties to assisting drug discovery to advancing cybersecurity. Recently, we added to this list by showing how a machine learning algorithm (a so-called learner) combined with an optimization routine can assist experimental efforts in the realm of tuning semiconductor quantum dot (QD) devices. Among other applications, semiconductor QDs are a candidate system for building quantum computers. The present-day tuning techniques for bringing the QD devices into a desirable configuration suitable for quantum computing that rely on heuristics do not scale with the increasing size of the quantum dot arrays required for even near-term quantum computing demonstrations. Establishing a reliable protocol for tuning that does not rely on the gross-scale heuristics developed by experimentalists is thus of great importance. To implement the machine learning-based approach, we constructed a dataset of simulated QD device characteristics, such as the conductance and the charge sensor response versus the applied electrostatic gate voltages. Here, we describe the methodology for generating the dataset, as well as its validation in training convolutional neural networks. We show that the learner's accuracy in recognizing the state of a device is ~96.5 % in both current- and charge-sensor-based training. We also introduce a tool that enables other researchers to use this approach for further research: QFlow lite - a Python-based mini-software suite that uses the dataset to train neural networks to recognize the state of a device and differentiate between states in experimental data. This work gives the definitive reference for the new dataset that will help enable researchers to use it in their experiments or to develop new machine learning approaches and concepts

%B PLOS ONE %V 13 %P e0205844 %8 2018 %G eng %U https://arxiv.org/abs/1809.10018 %N 10 %9 2018/10/17 %R https://doi.org/10.1371/journal.pone.0205844 %0 Journal Article %J Proc. ACM Program. Lang. %D 2018 %T Quantitative Robustness Analysis of Quantum Programs (Extended Version) %A Shih-Han Hung %A Kesha Hietala %A Shaopeng Zhu %A Mingsheng Ying %A Michael Hicks %A Xiaodi Wu %XQuantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources (e.g., qubits) are scarce, classical error correction techniques applied at the level of the architecture are currently cost-prohibitive. But while this reality means that quantum programs are almost certain to have errors, there as yet exists no principled means to reason about erroneous behavior. This paper attempts to fill this gap by developing a semantics for erroneous quantum while-programs, as well as a logic for reasoning about them. This logic permits proving a property we have identified, called ε-robustness, which characterizes possible "distance" between an ideal program and an erroneous one. We have proved the logic sound, and showed its utility on several case studies, notably: (1) analyzing the robustness of noisy versions of the quantum Bernoulli factory (QBF) and quantum walk (QW); (2) demonstrating the (in)effectiveness of different error correction schemes on single-qubit errors; and (3) analyzing the robustness of a fault-tolerant version of QBF.

%B Proc. ACM Program. Lang. %V 3 %P Article 31 %8 2018/12/1 %G eng %U https://arxiv.org/abs/1811.03585 %N POPL %R https://doi.org/10.1145/3290344 %0 Journal Article %D 2018 %T Quantum adiabatic optimization without heuristics %A Michael Jarret %A Brad Lackey %A Aike Liu %A Kianna Wan %XQuantum adiabatic optimization (QAO) is performed using a time-dependent Hamiltonian H(s) with spectral gap γ(s). Assuming the existence of an oracle Γ such that γ(s)=Θ(Γ(s)), we provide an algorithm that reliably performs QAO in time Oγ−1minlog(γ−1min) with Olog(γ−1min) oracle queries, where γmin=minsγ(s). Our strategy is not heuristic and does not require guessing time parameters or annealing paths. Rather, our algorithm naturally produces an annealing path such that dH/ds≈γ(s) and chooses its own runtime T to be as close as possible to optimal while promising convergence to the ground state. We then demonstrate the feasibility of this approach in practice by explicitly constructing a gap oracle Γ for the problem of finding a vertex m=argminuW(u) of the cost function W:V⟶[0,1], restricting ourselves to computational basis measurements and driving Hamiltonian H(0)=I−V−1∑u,v∈V|u⟩⟨v|, with V=|V|. Requiring only that W have a constant lower bound on its spectral gap and upper bound κ on its spectral ratio, our QAO algorithm returns m using Γ with probability (1−ε)(1−e−1/ε) in time O˜(ε−1[V−−√+(κ−1)2/3V2/3]). This achieves a quantum advantage for all κ, and when κ≈1, recovers Grover scaling up to logarithmic factors. We implement the algorithm as a subroutine in an optimization procedure that produces m with exponentially small failure probability and expected runtime O˜(ε−1[V−−√+(κ−1)2/3V2/3]), even when κ is not known beforehand.

%G eng %U https://arxiv.org/abs/1810.04686 %0 Journal Article %J Proceedings of The Royal Society A %D 2018 %T Quantum algorithm for multivariate polynomial interpolation %A Jianxin Chen %A Andrew M. Childs %A Shih-Han Hung %XHow many quantum queries are required to determine the coefficients of a degree-d polynomial in n variables? We present and analyze quantum algorithms for this multivariate polynomial interpolation problem over the fields Fq, R, and C. We show that kC and 2kC queries suffice to achieve probability 1 for C and R, respectively, where kC = ⌈ 1 n+1 ( n+d d )⌉ except for d = 2 and four other special cases. For Fq, we show that ⌈ d n+d ( n+d d )⌉ queries suffice to achieve probability approaching 1 for large field order q. The classical query complexity of this problem is ( n+d d ), so our result provides a speedup by a factor of n + 1, n+1 2 , and n+d d for C, R, and Fq, respectively. Thus we find a much larger gap between classical and quantum algorithms than the univariate case, where the speedup is by a factor of 2. For the case of Fq, we conjecture that 2kC queries also suffice to achieve probability approaching 1 for large field order q, although we leave this as an open problem.

%B Proceedings of The Royal Society A %V 474 %8 2018/01/17 %G eng %U http://rspa.royalsocietypublishing.org/content/474/2209/20170480 %N 2209 %R 10.1098/rspa.2017.0480 %0 Journal Article %D 2018 %T Quantum algorithms and lower bounds for convex optimization %A Shouvanik Chakrabarti %A Andrew M. Childs %A Tongyang Li %A Xiaodi Wu %XWhile recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a convex function over an n-dimensional convex body using O~(n) queries to oracles that evaluate the objective function and determine membership in the convex body. This represents a quadratic improvement over the best-known classical algorithm. We also study limitations on the power of quantum computers for general convex optimization, showing that it requires Ω~(n−−√) evaluation queries and Ω(n−−√) membership queries.

%G eng %U https://arxiv.org/abs/1809.01731 %0 Journal Article %D 2018 %T Quantum Channel Simulation and the Channel's Smooth Max-Information %A Kun Fang %A Xin Wang %A Marco Tomamichel %A Mario Berta %XWe study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot quantum simulation cost under no-signalling assisted codes are given by semidefinite programs. Second, we introduce the channel's smooth max-information, which can be seen as a one-shot generalization of the mutual information of a quantum channel. We provide an exact operational interpretation of the channel's smooth max-information as the one-shot quantum simulation cost under no-signalling assisted codes. Third, we derive the asymptotic equipartition property of the channel's smooth max-information, i.e., it converges to the quantum mutual information of the channel in the independent and identically distributed asymptotic limit. This implies the quantum reverse Shannon theorem in the presence of no-signalling correlations. Finally, we explore the simulation cost of various quantum channels.

%G eng %U https://arxiv.org/abs/1807.05354 %0 Journal Article %J IEEE Security & Privacy %D 2018 %T Quantum Cryptanalysis: Shor, Grover, and Beyond %A Stephen P. Jordan %A Yi-Kai Liu %B IEEE Security & Privacy %V 16 %P 14-21 %8 2018/09 %G eng %N 5 %R 10.1109/MSP.2018.3761719 %0 Journal Article %J Phys. Rev. %D 2018 %T Quantum field theory for the chiral clock transition in one spatial dimension %A Seth Whitsitt %A Rhine Samajdar %A Subir Sachdev %XWe describe the quantum phase transition in the N-state chiral clock model in spatial dimension d=1. With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and N=3, the clock model is expected to have a direct phase transition from a gapped phase with a broken global ZN symmetry, to a gapped phase with the ZN symmetry restored. The transition has dynamical critical exponent z≠1, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in d=1, involving the onset of a single boson condensate in the background of a higher-dimensional N-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in 2−d, with 4−N chosen to be of order 2−d. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for N=3, finding good evidence for a direct phase transition, and obtain estimates for z and the correlation length exponent ν.

%B Phys. Rev. %V B %P 205118 %8 2018/11/09 %G eng %U https://arxiv.org/abs/1808.07056 %N 98 %R https://doi.org/10.1103/PhysRevB.98.205118 %0 Journal Article %D 2018 %T Quantum generalizations of the polynomial hierarchy with applications to QMA(2) %A Sevag Gharibian %A Miklos Santha %A Jamie Sikora %A Aarthi Sundaram %A Justin Yirka %XThe polynomial-time hierarchy (PH) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as PH does not collapse). Here, we study whether two quantum generalizations of PH can similarly prove separations in the quantum setting. The first generalization, QCPH, uses classical proofs, and the second, QPH, uses quantum proofs. For the former, we show quantum variants of the Karp-Lipton theorem and Toda's theorem. For the latter, we place its third level, QΣ3, into NEXP {using the Ellipsoid Method for efficiently solving semidefinite programs}. These results yield two implications for QMA(2), the variant of Quantum Merlin-Arthur (QMA) with two unentangled proofs, a complexity class whose characterization has proven difficult. First, if QCPH=QPH (i.e., alternating quantifiers are sufficiently powerful so as to make classical and quantum proofs "equivalent"), then QMA(2) is in the Counting Hierarchy (specifically, in PPPPP). Second, unless QMA(2)=QΣ3 (i.e., alternating quantifiers do not help in the presence of "unentanglement"), QMA(2) is strictly contained in NEXP.

%G eng %U https://arxiv.org/abs/1805.11139 %0 Journal Article %D 2018 %T Quantum Probability Estimation for Randomness with Quantum Side Information %A Emanuel Knill %A Yanbao Zhang %A Honghao Fu %XWe develop a quantum version of the probability estimation framework [arXiv:1709.06159] for randomness generation with quantum side information. We show that most of the properties of probability estimation hold for quantum probability estimation (QPE). This includes asymptotic optimality at constant error and randomness expansion with logarithmic input entropy. QPE is implemented by constructing model-dependent quantum estimation factors (QEFs), which yield statistical confidence upper bounds on data-conditional normalized Rényi powers. This leads to conditional min-entropy estimates for randomness generation. The bounds are valid for relevant models of sequences of experimental trials without requiring independent and identical or stationary behavior. QEFs may be adapted to changing conditions during the sequence and trials can be stopped any time, such as when the results so far are satisfactory. QEFs can be constructed from entropy estimators to improve the bounds for conditional min-entropy of classical-quantum states from the entropy accumulation framework [Dupuis, Fawzi and Renner, arXiv:1607.01796]. QEFs are applicable to a larger class of models, including models permitting measurement devices with super-quantum but non-signaling behaviors and semi-device dependent models. The improved bounds are relevant for finite data or error bounds of the form e−κs, where s is the number of random bits produced. We give a general construction of entropy estimators based on maximum probability estimators, which exist for many configurations. For the class of (k,2,2) Bell-test configurations we provide schemas for directly optimizing QEFs to overcome the limitations of entropy-estimator-based constructions. We obtain and apply QEFs for examples involving the (2,2,2) Bell-test configuration to demonstrate substantial improvements in finite-data efficiency.

%G eng %U https://arxiv.org/abs/1806.04553 %0 Journal Article %D 2018 %T Quantum SDP Solvers: Large Speed-ups, Optimality, and Applications to Quantum Learning %A Fernando G. S. L. Brandão %A Amir Kalev %A Tongyang Li %A Cedric Yen-Yu Lin %A Krysta M. Svore %A Xiaodi Wu %XWe give two new quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with m constraint matrices, each of dimension n, rank r, and sparsity s. The first algorithm assumes an input model where one is given access to entries of the matrices at unit cost. We show that it has run time O~(s2(m−−√ε−10+n−−√ε−12)), where ε is the error. This gives an optimal dependence in terms of m,n and quadratic improvement over previous quantum algorithms when m≈n. The second algorithm assumes a fully quantum input model in which the matrices are given as quantum states. We show that its run time is O~(m−−√+poly(r))⋅poly(logm,logn,B,ε−1), with B an upper bound on the trace-norm of all input matrices. In particular the complexity depends only poly-logarithmically in n and polynomially in r. We apply the second SDP solver to the problem of learning a good description of a quantum state with respect to a set of measurements: Given m measurements and copies of an unknown state ρ, we show we can find in time m−−√⋅poly(logm,logn,r,ε−1) a description of the state as a quantum circuit preparing a density matrix which has the same expectation values as ρ on the m measurements, up to error ε. The density matrix obtained is an approximation to the maximum entropy state consistent with the measurement data considered in Jaynes' principle from statistical mechanics. As in previous work, we obtain our algorithm by "quantizing" classical SDP solvers based on the matrix multiplicative weight method. One of our main technical contributions is a quantum Gibbs state sampler for low-rank Hamiltonians with a poly-logarithmic dependence on its dimension, which could be of independent interest.

%G eng %U https://arxiv.org/abs/1710.02581 %0 Journal Article %J Proceedings of the 51st ACM Symposium on Theory of Computing (to appear) %D 2018 %T Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics %A Andras Gilyen %A Yuan Su %A Guang Hao Low %A Nathan Wiebe %XQuantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation" algorithm capable of harnessing this exponential advantage, that can apply polynomial transformations to the singular values of a block of a unitary, generalizing the optimal Hamiltonian simulation results of Low and Chuang. The proposed quantum circuits have a very simple structure, often give rise to optimal algorithms and have appealing constant factors, while usually only use a constant number of ancilla qubits. We show that singular value transformation leads to novel algorithms. We give an efficient solution to a certain "non-commutative" measurement problem and propose a new method for singular value estimation. We also show how to exponentially improve the complexity of implementing fractional queries to unitaries with a gapped spectrum. Finally, as a quantum machine learning application we show how to efficiently implement principal component regression. "Singular value transformation" is conceptually simple and efficient, and leads to a unified framework of quantum algorithms incorporating a variety of quantum speed-ups. We illustrate this by showing how it generalizes a number of prominent quantum algorithms, including: optimal Hamiltonian simulation, implementing the Moore-Penrose pseudoinverse with exponential precision, fixed-point amplitude amplification, robust oblivious amplitude amplification, fast QMA amplification, fast quantum OR lemma, certain quantum walk results and several quantum machine learning algorithms. In order to exploit the strengths of the presented method it is useful to know its limitations too, therefore we also prove a lower bound on the efficiency of singular value transformation, which often gives optimal bounds.

%B Proceedings of the 51st ACM Symposium on Theory of Computing (to appear) %8 2018/06/05 %G eng %U https://arxiv.org/abs/1806.01838 %0 Journal Article %D 2018 %T Quantum Supremacy and the Complexity of Random Circuit Sampling %A Adam Bouland %A Bill Fefferman %A Chinmay Nirkhe %A Umesh Vazirani %XA critical milestone on the path to useful quantum computers is quantum supremacy - a demonstration of a quantum computation that is prohibitively hard for classical computers. A leading near-term candidate, put forth by the Google/UCSB team, is sampling from the probability distributions of randomly chosen quantum circuits, which we call Random Circuit Sampling (RCS). In this paper we study both the hardness and verification of RCS. While RCS was defined with experimental realization in mind, we show complexity theoretic evidence of hardness that is on par with the strongest theoretical proposals for supremacy. Specifically, we show that RCS satisfies an average-case hardness condition - computing output probabilities of typical quantum circuits is as hard as computing them in the worst-case, and therefore #P-hard. Our reduction exploits the polynomial structure in the output amplitudes of random quantum circuits, enabled by the Feynman path integral. In addition, it follows from known results that RCS satisfies an anti-concentration property, making it the first supremacy proposal with both average-case hardness and anti-concentration.

%G eng %U https://arxiv.org/abs/1803.04402 %0 Journal Article %D 2018 %T Quantum-secure message authentication via blind-unforgeability %A Gorjan Alagic %A Christian Majenz %A Alexander Russell %A Fang Song %XFormulating and designing unforgeable authentication of classical messages in the presence of quantum adversaries has been a challenge, as the familiar classical notions of unforgeability do not directly translate into meaningful notions in the quantum setting. A particular difficulty is how to fairly capture the notion of "predicting an unqueried value" when the adversary can query in quantum superposition. In this work, we uncover serious shortcomings in existing approaches, and propose a new definition. We then support its viability by a number of constructions and characterizations. Specifically, we demonstrate a function which is secure according to the existing definition by Boneh and Zhandry, but is clearly vulnerable to a quantum forgery attack, whereby a query supported only on inputs that start with 0 divulges the value of the function on an input that starts with 1. We then propose a new definition, which we call "blind-unforgeability" (or BU.) This notion matches "intuitive unpredictability" in all examples studied thus far. It defines a function to be predictable if there exists an adversary which can use "partially blinded" oracle access to predict values in the blinded region. Our definition (BU) coincides with standard unpredictability (EUF-CMA) in the classical-query setting. We show that quantum-secure pseudorandom functions are BU-secure MACs. In addition, we show that BU satisfies a composition property (Hash-and-MAC) using "Bernoulli-preserving" hash functions, a new notion which may be of independent interest. Finally, we show that BU is amenable to security reductions by giving a precise bound on the extent to which quantum algorithms can deviate from their usual behavior due to the blinding in the BU security experiment.

%G eng %U https://arxiv.org/abs/1803.03761 %0 Journal Article %J Phys. Rev. %D 2018 %T The quasiprobability behind the out-of-time-ordered correlator %A Nicole Yunger Halpern %A Brian Swingle %A Justin Dressel %XTwo topics, evolving rapidly in separate fields, were combined recently: The out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC has been shown to equal a moment of a summed quasiprobability. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability's structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze the weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse-graining) numerically and analytically: We simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits, which model chaotic dynamics. The quasiprobability, we find, distinguishes chaotic from integrable regimes. We observe nonclassical behaviors: The quasiprobability typically has negative components. It becomes nonreal in some regimes. The onset of scrambling breaks a symmetry that bifurcates the quasiprobability, as in classical-chaos pitchforks. Finally, we present mathematical properties. The quasiprobability obeys a Bayes-type theorem, for example, that exponentially decreases the memory required to calculate weak values, in certain cases. A time-ordered correlator analogous to the OTOC, insensitive to quantum-information scrambling, depends on a quasiprobability closer to a classical probability. This work not only illuminates the OTOC's underpinnings, but also generalizes quasiprobability theory and motivates immediate-future weak-measurement challenges.

%B Phys. Rev. %V A %8 04/2018 %G eng %U https://arxiv.org/abs/1704.01971 %N 97 %& 042105 %R https://doi.org/10.1103/PhysRevA.97.042105 %0 Journal Article %J Phys. Rev. Lett. %D 2018 %T Recovering quantum gates from few average gate fidelities %A Ingo Roth %A Richard Kueng %A Shelby Kimmel %A Yi-Kai Liu %A David Gross %A Jens Eisert %A Martin Kliesch %XCharacterising quantum processes is a key task in and constitutes a challenge for the development of quantum technologies, especially at the noisy intermediate scale of today's devices. One method for characterising processes is randomised benchmarking, which is robust against state preparation and measurement (SPAM) errors, and can be used to benchmark Clifford gates. A complementing approach asks for full tomographic knowledge. Compressed sensing techniques achieve full tomography of quantum channels essentially at optimal resource efficiency. So far, guarantees for compressed sensing protocols rely on unstructured random measurements and can not be applied to the data acquired from randomised benchmarking experiments. It has been an open question whether or not the favourable features of both worlds can be combined. In this work, we give a positive answer to this question. For the important case of characterising multi-qubit unitary gates, we provide a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured respect to random Clifford unitaries. Moreover, for general unital quantum channels we provide an explicit expansion into a unitary 2-design, allowing for a practical and guaranteed reconstruction also in that case. As a side result, we obtain a new statistical interpretation of the unitarity -- a figure of merit that characterises the coherence of a process. In our proofs we exploit recent representation theoretic insights on the Clifford group, develop a version of Collins' calculus with Weingarten functions for integration over the Clifford group, and combine this with proof techniques from compressed sensing.

%B Phys. Rev. Lett. %V 121 %P 170502 %8 2018/03/01 %G eng %U https://arxiv.org/abs/1803.00572 %R https://doi.org/10.1103/PhysRevLett.121.170502 %0 Journal Article %D 2018 %T Recovery Map for Fermionic Gaussian Channels %A Brian Swingle %A Yixu Wang %XA recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are convenient because they are totally determined by their covariance matrix and because they form a closed set under so-called Gaussian channels. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel. As a by-product, we obtain a formula for the fidelity between two fermionic Gaussian states. We also discuss subtleties arising from the singularities of the involved matrices.

%G eng %U https://arxiv.org/abs/1811.04956 %0 Journal Article %J Phys. Rev. %D 2018 %T Resilience of scrambling measurements %A Brian Swingle %A Nicole Yunger Halpern %XMost experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backwards time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum-chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.

%B Phys. Rev. %V A %8 2018/06/18 %G eng %U https://arxiv.org/abs/1802.01587 %N 97 %& 062113 %R https://doi.org/10.1103/PhysRevA.97.062113 %0 Journal Article %J Science %D 2018 %T Resonantly driven CNOT gate for electron spins %A D. M. Zajac %A A. J. Sigillito %A M. Russ %A F. Borjans %A J. M. Taylor %A Guido Burkard %A J. R. Petta %XSingle-qubit rotations and two-qubit CNOT operations are crucial ingredients for universal quantum computing. Although high-fidelity single-qubit operations have been achieved using the electron spin degree of freedom, realizing a robust CNOT gate has been challenging because of rapid nuclear spin dephasing and charge noise. We demonstrate an efficient resonantly driven CNOT gate for electron spins in silicon. Our platform achieves single-qubit rotations with fidelities greater than 99%, as verified by randomized benchmarking. Gate control of the exchange coupling allows a quantum CNOT gate to be implemented with resonant driving in ~200 nanoseconds. We used the CNOT gate to generate a Bell state with 78% fidelity (corrected for errors in state preparation and measurement). Our quantum dot device architecture enables multi-qubit algorithms in silicon.

%B Science %V 359 %P 439-442 %8 2018/01/26 %G eng %U http://science.sciencemag.org/content/359/6374/439 %N 6374 %R 10.1126/science.aao5965 %0 Journal Article %J Physical Review Letters %D 2018 %T Robust two-qubit gates in a linear ion crystal using a frequency-modulated driving force %A Pak Hong Leung %A Kevin A. Landsman %A Caroline Figgatt %A Norbert M. Linke %A Christopher Monroe %A Kenneth R. Brown %XIn an ion trap quantum computer, collective motional modes are used to entangle two or more qubits in order to execute multi-qubit logical gates. Any residual entanglement between the internal and motional states of the ions will result in decoherence errors, especially when there are many spectator ions in the crystal. We propose using a frequency-modulated (FM) driving force to minimize such errors and implement it experimentally. In simulation, we obtained an optimized FM gate that can suppress decoherence to less than 10−4 and is robust against a frequency drift of more than ±1 kHz. The two-qubit gate was tested in a five-qubit trapped ion crystal, with 98.3(4)% fidelity for a Mølmer-Sørensen entangling gate and 98.6(7)% for a controlled-not (CNOT) gate. We also show an optimized FM two-qubit gate for 17 ions, proving the scalability of our method.

%B Physical Review Letters %V 120 %P 020501 %8 2018/01/09 %G eng %U https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.020501 %N 2 %R 10.1103/PhysRevLett.120.020501 %0 Journal Article %D 2018 %T Scrambling dynamics across a thermalization-localization quantum phase transition %A Subhayan Sahu %A Shenglong Xu %A Brian Swingle %XWe study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with sub-ballistic operator spreading. The critical disorder strength for the ballistic to sub-ballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, we find that the operator dynamics is not very sensitive to the actual eigenstate localization transition. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.

%G eng %U https://arxiv.org/abs/1807.06086 %0 Journal Article %D 2018 %T A semiclassical theory of phase-space dynamics of interacting bosons %A Ranchu Mathew %A Eite Tiesinga %XWe study the phase-space representation of dynamics of bosons in the semiclassical regime where the occupation number of the modes is large. To this end, we employ the van Vleck-Gutzwiller propagator to obtain an approximation for the Green's function of the Wigner distribution. The semiclassical analysis incorporates interference of classical paths and reduces to the truncated Wigner approximation (TWA) when the interference is ignored. Furthermore, we identify the Ehrenfest time after which the TWA fails. As a case study, we consider a single-mode quantum nonlinear oscillator, which displays collapse and revival of observables. We analytically show that the interference of classical paths leads to revivals, an effect that is not reproduced by the TWA or a perturbative analysis.

%G eng %U https://arxiv.org/abs/1803.05122 %0 Journal Article %D 2018 %T Single-photon bound states in atomic ensembles %A Yidan Wang %A Michael J. Gullans %A Antoine Browaeys %A J. V. Porto %A Darrick E. Chang %A Alexey V. Gorshkov %XWe illustrate the existence of single-excitation bound states for propagating photons interacting with N two-level atoms. These bound states can be calculated from an effective spin model, and their existence relies on dissipation in the system. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission and with divergent bunching in the second-order photon-photon correlation function. We also formulate a dissipative version of Levinson's theorem for this system by looking at the relation between the number of bound states and the winding number of the transmission phases. This theorem allows a direct experimental measurement of the number of bound states using the measured transmission phases.

%G eng %U https://arxiv.org/abs/1809.01147 %0 Journal Article %D 2018 %T Spectrum estimation of density operators with alkaline-earth atoms %A Michael E. Beverland %A Jeongwan Haah %A Gorjan Alagic %A Gretchen K. Campbell %A Ana Maria Rey %A Alexey V. Gorshkov %XWe show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose *n *copies are stored in the nuclear spins of *n *such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing, quantum simulation, and time-keeping with alkalineearth atoms are discussed.

The SU(1,1) interferometer was originally conceived as a Mach-Zehnder interferometer with the beam-splitters replaced by parametric amplifiers. The parametric amplifiers produce states with correlations that result in enhanced phase sensitivity. F=1 spinor Bose-Einstein condensates (BECs) can serve as the parametric amplifiers for an atomic version of such an interferometer by collisionally producing entangled pairs of ⟨F=1,m=±1| atoms. We simulate the effect of single and double-sided seeding of the inputs to the amplifier using the truncated-Wigner approximation. We find that single-sided seeding degrades the performance of the interferometer exactly at the phase the unseeded interferometer should operate the best. Double-sided seeding results in a phase-sensitive amplifier, where the maximal sensitivity is a function of the phase relationship between the input states of the amplifier. In both single and double-sided seeding we find there exists an optimal phase shift that achieves sensitivity beyond the standard quantum limit. Experimentally, we demonstrate a spinor phase-sensitive amplifier using a BEC of 23Na in an optical dipole trap. This configuration could be used as an input to such an interferometer. We are able to control the initial phase of the double-seeded amplifier, and demonstrate sensitivity to initial population fractions as small as 0.1\%.

%B Phys. Rev %V A 98 %G eng %U https://arxiv.org/abs/1807.06676 %N 023620 %0 Journal Article %D 2018 %T Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits %A Lucas Kocia %A Peter Love %XWe apply the periodized stationary phase method to discrete Wigner functions of systems with odd prime dimension using results from p-adic number theory. We derive the Wigner-Weyl-Moyal (WWM) formalism with higher order ℏ corrections representing contextual corrections to non-contextual Clifford operations. We apply this formalism to a subset of unitaries that include diagonal gates such as the π8 gates. We characterize the stationary phase critical points as a quantum resource injecting contextuality and show that this resource allows for the replacement of the p2t points that represent t magic state Wigner functions on p-dimensional qudits by ≤pt points. We find that the π8 gate introduces the smallest higher order ℏ correction possible, requiring the lowest number of additional critical points compared to the Clifford gates. We then establish a relationship between the stabilizer rank of states and the number of critical points necessary to treat them in the WWM formalism. This allows us to exploit the stabilizer rank decomposition of two qutrit π8 gates to develop a classical strong simulation of a single qutrit marginal on t qutrit π8 gates that are followed by Clifford evolution, and show that this only requires calculating 3t2+1 critical points corresponding to Gauss sums. This outperforms the best alternative qutrit algorithm (based on Wigner negativity and scaling as ∼30.8t for 10−2 precision) for any number of π8 gates to full precision.

%G eng %U https://arxiv.org/abs/1810.03622 %0 Journal Article %J Phys. Rev. %D 2018 %T Structure of Correlated Worldline Theories of Quantum Gravity %A Andrei O. Barvinsky %A Daniel Carney %A Philip C. E. Stamp %XWe consider the general form of "Correlated Worldline" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple copies of the coupled matter and gravitational fields. In both versions, the paths in a functional formulation are correlated via gravity itself, causing a breakdown of the superposition principle; however, the product form survives consistency tests not satisfied by the summed form. To better understand the structure of these two theories, we show how to perform diagrammatic expansions in the gravitational coupling for each version of CWL theory, using particle propagation and scalar fields as examples. We explicitly calculate contributions to 2-point and 4-point functions, again for each version of the theory, up to 2nd-order in the gravitational coupling.

%B Phys. Rev. %V D %P 084052 %8 2018/06/21 %G eng %U https://arxiv.org/abs/1806.08043 %N 98 %R https://doi.org/10.1103/PhysRevD.98.084052 %0 Journal Article %D 2018 %T Study of radon reduction in gases for rare event search experiments %A K. Pushkin %A C. Akerlof %A D. Anbajagane %A J. Armstrong %A M. Arthurs %A J. Bringewatt %A T. Edberg %A C. Hall %A M. Lei %A R. Raymond %A M. Reh %A D. Saini %A A. Sander %A J. Schaefer %A D. Seymour %A N. Swanson %A Y. Wang %A W. Lorenzon %XThe noble elements, argon and xenon, are frequently employed as the target and event detector for weakly interacting particles such as neutrinos and Dark Matter. For such rare processes, background radiation must be carefully minimized. Radon provides one of the most significant contaminants since it is an inevitable product of trace amounts of natural uranium. To design a purification system for reducing such contamination, the adsorption characteristics of radon in nitrogen, argon, and xenon carrier gases on various types of charcoals with different adsorbing properties and intrinsic radioactive purities have been studied in the temperature range of 190-295 K at flow rates of 0.5 and 2 standard liters per minute. Essential performance parameters for the various charcoals include the average breakthrough times (

Research shows that community plays a central role in learning, and strong community engages students and aids in student persistence. Thus, understanding the function and structure of communities in learning environments is essential to education. We use social network analysis to explore the community dynamics of students in a pre-matriculation, two-week summer program. Unlike previous network analysis studies in PER, we build our networks from classroom video that has been coded for student interactions using labeled, directed ties. We define 3 types of interaction: on task interactions (regarding the assigned task), on topic interactions (having to do with science, technology, engineering, and mathematics (STEM)), and off topic interactions (unrelated to the assignment or STEM). To study the development of community in this program, we analyze the shift in conversation topicality over the course of the program. Conversations are more on-task toward the end of the program and we propose that this conversational shift represents a change in student membership within their forming community.

%G eng %U https://arxiv.org/abs/1808.08193 %0 Journal Article %D 2018 %T Subsystem Complexity and Holography %A Cesar A. Agón %A Matthew Headrick %A Brian Swingle %XWe study circuit complexity for spatial regions in holographic field theories. We study analogues based on the entanglement wedge of the bulk quantities appearing in the "complexity = volume" and "complexity = action" conjectures. We calculate these quantities for one exterior region of an eternal static neutral or charged black hole in general dimensions, dual to a thermal state on one boundary with or without chemical potential respectively, as well as for a shock wave geometry. We then define several analogues of circuit complexity for mixed states, and use tensor networks to gain intuition about them. We find a promising qualitative match between the holographic action and what we call the purification complexity, the minimum number of gates required to prepare an arbitrary purification of the given mixed state. On the other hand, the holographic volume does not appear to match any of our definitions of mixed-state complexity.

%G eng %U https://arxiv.org/abs/1804.01561 %0 Journal Article %D 2018 %T Tabletop experiments for quantum gravity: a user's manual %A Daniel Carney %A Philip C. E. Stamp %A Jacob M. Taylor %XRecent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

%G eng %U https://arxiv.org/abs/1807.11494 %0 Journal Article %D 2018 %T Tabletop experiments for quantum gravity: a user's manual %A Daniel Carney %A Philip C. E. Stamp %A Jacob M. Taylor %XRecent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

%G eng %U https://arxiv.org/abs/1807.11494 %0 Journal Article %J Quantum %D 2018 %T Time-reversal of rank-one quantum strategy functions %A Yuan Su %A John Watrous %XThe quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a class of linear functions, defined on quantum strategy representations within this framework, that corresponds to the set of rank-one positive semidefinite operators on a certain space. This time-reversal property states that the maximum value obtained by such a function over all valid quantum strategies is also obtained when the direction of time for the function is reversed, despite the fact that the strategies themselves are generally not time reversible. An application of this fact is an alternative proof of a known relationship between the conditional min- and max-entropy of bipartite quantum states, along with generalizations of this relationship.

%B Quantum %V 2 %8 2018/01/25 %G eng %U https://arxiv.org/abs/1801.08491 %N 98 %R https://doi.org/10.22331/q-2018-10-04-98 %0 Book %D 2018 %T Totally random: why nobody understands quantum mechanics (a serious comic on entanglement) %A Jeffrey Bub %A Tanya Bub %I Princeton University Press %G eng %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2018 %T Toward the first quantum simulation with quantum speedup %A Andrew M. Childs %A Dmitri Maslov %A Yunseong Nam %A Neil J. Ross %A Yuan Su %XWith quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin systems, which could be applied to understand condensed matter phenomena. We synthesize explicit circuits for three leading quantum simulation algorithms, using diverse techniques to tighten error bounds and optimize circuit implementations. Quantum signal processing appears to be preferred among algorithms with rigorous performance guarantees, whereas higher-order product formulas prevail if empirical error estimates suffice. Our circuits are orders of magnitude smaller than those for the simplest classically infeasible instances of factoring and quantum chemistry, bringing practical quantum computation closer to reality.

%B Proceedings of the National Academy of Sciences %V 115 %P 9456-9461 %G eng %U https://arxiv.org/abs/1711.10980 %R https://doi.org/10.1073/pnas.1801723115 %0 Journal Article %D 2018 %T Two Dimensional Dilaton Gravity Theory and Lattice Schwarzian Theory %A Su-Kuan Chu %A Chen-Te Ma %A Chih-Hung Wu %XWe report a holographic study of a two dimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of non-vanishing and vanishing cosmological constants. Our result shows that a boundary theory of the two dimensional dilaton gravity theory with the Dirichlet boundary condition for the case of a non-vanishing cosmological constant is a Schwarzian term coupled to a dilaton field, while for the case of a vanishing cosmological constant, it is a trivial theory that does not have a kinetic term. We also include the higher derivative term R2, where R is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the second order perturbation of the boundary cut-off ε2 under a constant boundary dilaton field and the non-vanishing cosmological constant by identifying the lattice spacing a of a lattice Schwarzian theory with the boundary cut-off ε of the two dimensional dilaton gravity theory.

%G eng %U https://arxiv.org/abs/1802.04599 %0 Journal Article %D 2018 %T Unitary Entanglement Construction in Hierarchical Networks %A Aniruddha Bapat %A Zachary Eldredge %A James R. Garrison %A Abhinav Desphande %A Frederic T. Chong %A Alexey V. Gorshkov %XThe construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement--the translation from circuit diagrams to machine qubits--on quantum systems whose connectivity is described by hierarchies.

%G eng %U https://arxiv.org/abs/1808.07876 %0 Journal Article %D 2018 %T Validating and Certifying Stabilizer States %A Amir Kalev %A Anastasios Kyrillidis %XWe propose a measurement scheme that validates the preparation of a target n-qubit stabilizer state. The scheme involves a measurement of n Pauli observables, a priori determined from the target stabilizer and which can be realized using single-qubit gates. Based on the proposed validation scheme, we derive an explicit expression for the worse-case fidelity, i.e., the minimum fidelity between the target stabilizer state and any other state consistent with the measured data. We also show that the worse-case fidelity can be certified, with high probability, using O(n) copies of the state of the system per measured observable.

%G eng %U https://arxiv.org/abs/1808.10786 %0 Journal Article %D 2018 %T Verified Quantum Information Scrambling %A Kevin A. Landsman %A Caroline Figgatt %A Thomas Schuster %A Norbert M. Linke %A Beni Yoshida %A Norman Y. Yao %A Christopher Monroe %XQuantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout the entire system. This concept underlies the dynamics of thermalization in closed quantum systems, and more recently has emerged as a powerful tool for characterizing chaos in black holes. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, since scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here, we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous litmus test for scrambling while projecting potential circuit errors into an ancillary observable. We engineer quantum scrambling processes through a tunable 3-qubit unitary operation as part of a 7-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically ∼80%, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.

%G eng %U https://arxiv.org/abs/1806.02807 %0 Journal Article %J Nature Communications %D 2017 %T Above threshold scattering about a Feshbach resonance for ultracold atoms in an optical collider %A Milena S. J. Horvath %A Ryan Thomas %A Eite Tiesinga %A Amita B. Deb %A Niels Kjærgaard %XStudies of magnetically tunable Feshbach resonances in ultracold atomic gases have predominantly been carried out in the zero collision-energy limit. Here, we explore above threshold collisions at well-defined energies in the vicinity of a narrow magnetic Feshbach resonance by means of a laser-based collider. Our experiment focuses on collisions between ground-state 87Rb atoms in the |F = 2,mF = 0i and |F = 1,mF = 1i hyperfine states, which have a known s-wave resonance at 9.040(7) G at threshold that strongly couples to inelastic channels, where 1 G = 10−4 T. Using our collider we can track the magnetic field shift in resonance position as the energy is tuned. This presents a challenge due to the narrow width of the resonance in conjunction with inherent broadening mechanisms of the collider. We find, however, that the narrow Feshbach scattering feature becomes imprinted on the spatial distribution of atoms in a fashion that allows for an accurate determination of resonance position as a function of collision energy through a shift in center-of-mass position of the outgoing clouds. This shift has a dispersive line shape with a zero value at the resonance position. We obtain excellent agreement with theory on the resonance position.

%B Nature Communications %V 8 %8 2017/09/06 %G eng %U https://arxiv.org/abs/1704.07109 %N 452 %R 10.1038/s41467-017-00458-y %0 Journal Article %J IEEE SMC, Banff, AB %D 2017 %T Advances in Quantum Reinforcement Learning %A Vedran Dunjko %A Jacob M. Taylor %A Hans J. Briegel %XIn recent times, there has been much interest in quantum enhancements of machine learning, specifically in the context of data mining and analysis. Reinforcement learning, an interactive form of learning, is, in turn, vital in artificial intelligence-type applications. Also in this case, quantum mechanics was shown to be useful, in certain instances. Here, we elucidate these results, and show that quantum enhancements can be achieved in a new setting: the setting of learning models which learn how to improve themselves -- that is, those that meta-learn. While not all learning models meta-learn, all non-trivial models have the potential of being "lifted", enhanced, to meta-learning models. Our results show that also such models can be quantum-enhanced to make even better learners. In parallel, we address one of the bottlenecks of current quantum reinforcement learning approaches: the need for so-called oracularized variants of task environments. Here we elaborate on a method which realizes these variants, with minimal changes in the setting, and with no corruption of the operative specification of the environments. This result may be important in near-term experimental demonstrations of quantum reinforcement learning.

%B IEEE SMC, Banff, AB %P 282-287 %8 2017 %G eng %U https://arxiv.org/abs/1811.08676 %R https://doi.org/10.1109/SMC.2017.8122616 %0 Journal Article %J New Journal of Physics %D 2017 %T Basic circuit compilation techniques for an ion-trap quantum machine %A Dmitri Maslov %XWe study the problem of compilation of quantum algorithms into optimized physical-level circuits executable in a quantum information processing (QIP) experiment based on trapped atomic ions. We report a complete strategy: starting with an algorithm in the form of a quantum computer program, we compile it into a high-level logical circuit that goes through multiple stages of decomposition into progressively lower-level circuits until we reach the physical execution-level specification. We skip the fault-tolerance layer, as it is not necessary in this work. The different stages are structured so as to best assist with the overall optimization while taking into account numerous optimization criteria, including minimizing the number of expensive two-qubit gates, minimizing the number of less expensive single-qubit gates, optimizing the runtime, minimizing the overall circuit error, and optimizing classical control sequences. Our approach allows a trade-off between circuit runtime and quantum error, as well as to accommodate future changes in the optimization criteria that may likely arise as a result of the anticipated improvements in the physical-level control of the experiment.

%B New Journal of Physics %V 19 %P 023035 %8 2016/02/20 %G eng %U http://iopscience.iop.org/article/10.1088/1367-2630/aa5e47/meta;jsessionid=55CC235A0B106081E825099310586F07.c3.iopscience.cld.iop.org %N 2 %R 10.1088/1367-2630/aa5e47 %0 Journal Article %J Nature Communications, accepted %D 2017 %T Complete 3-Qubit Grover Search on a Programmable Quantum Computer %A C. Figgatt %A Dmitri Maslov %A K. A. Landsman %A N. M. Linke %A S. Debnath %A Christopher Monroe %XSearching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. It is an optimal search algorithm for a quantum computer, and has further applications as a subroutine for other quantum algorithms. Searches with two qubits have been demonstrated on a variety of platforms and proposed for others, but larger search spaces have only been demonstrated on a non-scalable NMR system. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state-marking scheme required to perform a classical search. All quantum solutions are shown to outperform their classical counterparts. We also report the first implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5% and 89.6%, respectively.

%B Nature Communications, accepted %8 2017/03/30 %G eng %U https://arxiv.org/abs/1703.10535 %0 Journal Article %D 2017 %T Complexity of sampling as an order parameter %A Abhinav Deshpande %A Bill Fefferman %A Michael Foss-Feig %A Alexey V. Gorshkov %XWe consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time

We initiate the study of computational entropy in the quantum setting. We investigate to what extent the classical notions of computational entropy generalize to the quantum setting, and whether quantum analogues of classical theorems hold. Our main results are as follows. (1) The classical Leakage Chain Rule for pseudoentropy can be extended to the case that the leakage information is quantum (while the source remains classical). Specifically, if the source has pseudoentropy at least k, then it has pseudoentropy at least k − ℓ conditioned on an ℓ- qubit leakage. (2) As an application of the Leakage Chain Rule, we construct the first quantum leakage-resilient stream-cipher in the bounded-quantum-storage model, assuming the existence of a quantum-secure pseudorandom generator. (3) We show that the general form of the classical Dense Model Theorem (interpreted as the equivalence between two definitions of pseudo-relativemin-entropy) does not extend to quantum states. Along the way, we develop quantum analogues of some classical techniques (e.g., the Leakage Simulation Lemma, which is proven by a Nonuniform Min-Max Theorem or Boosting). On the other hand, we also identify some classical techniques (e.g., Gap Amplification) that do not work in the quantum setting. Moreover, we introduce a variety of notions that combine quantum information and quantum complexity, and this raises several directions for future work.

%8 2017/09/09 %G eng %U https://arxiv.org/abs/1704.07309 %0 Journal Article %J Physical Review Letters %D 2017 %T Cooling a harmonic oscillator by optomechanical modification of its bath %A Xunnong Xu %A Thomas Purdy %A Jacob M. Taylor %XOptomechanical systems show tremendous promise for high sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically-induced effect analogous to a phononic band gap. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme.

%B Physical Review Letters %V 118 %P 223602 %8 2017/05/31 %G eng %U https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.223602 %R doi.org/10.1103/PhysRevLett.118.223602 %0 Journal Article %J Physical Review Letters %D 2017 %T Correlated Photon Dynamics in Dissipative Rydberg Media %A Emil Zeuthen %A Michael Gullans %A Mohammad F. Maghrebi %A Alexey V. Gorshkov %XRydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging many-body problem in the limit of large optical depth per blockade radius. In our approach, we separate the single-polariton EIT physics from Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter, thus capturing the dualistic particle-wave nature of light as it manifests itself in dissipative Rydberg-EIT media. Using this approach, we analyze the saturation behavior of the transmission through one-dimensional Rydberg-EIT media in the regime of non-perturbative dissipative interactions relevant to current experiments. Our model is in good agreement with experimental data. We also analyze a scheme for generating regular trains of single photons from continuous-wave input and derive its scaling behavior in the presence of imperfect single-photon EIT.

%B Physical Review Letters %V 119 %P 043602 %8 2017/07/26 %G eng %U https://arxiv.org/abs/1608.06068 %N 4 %R 10.1103/PhysRevLett.119.043602 %0 Journal Article %J Metrologia %D 2017 %T Development of a new UHV/XHV pressure standard (cold atom vacuum standard) %A Julia Scherschligt %A James A Fedchak %A Daniel S Barker %A Stephen Eckel %A Nikolai Klimov %A Constantinos Makrides %A Eite Tiesinga %XThe National Institute of Standards and Technology has recently begun a program to develop a primary pressure standard that is based on ultra-cold atoms, covering a pressure range of 1 x 10-6 to 1 x 10-10 Pa and possibly lower. These pressures correspond to the entire ultra-high vacuum range and extend into the extreme-high vacuum. This cold-atom vacuum standard (CAVS) is both a primary standard and absolute sensor of vacuum. The CAVS is based on the loss of cold, sensor atoms (such as the alkali-metal lithium) from a magnetic trap due to collisions with the background gas (primarily H2) in the vacuum. The pressure is determined from a thermally-averaged collision cross section, which is a fundamental atomic property, and the measured loss rate. The CAVS is primary because it will use collision cross sections determined from ab initio calculations for the Li + H2 system. Primary traceability is transferred to other systems of interest using sensitivity coefficients.

%B Metrologia %V 54 %8 2017/11/3 %G eng %U https://arxiv.org/abs/1801.10120 %N 6 %R https://doi.org/10.1088/1681-7575/aa8a7b %0 Journal Article %J Physical Review B %D 2017 %T Disorder induced transitions in resonantly driven Floquet Topological Insulators %A Paraj Titum %A Netanel H. Lindner %A Gil Refael %XWe investigate the effects of disorder in Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are induced by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a mobility gap at the resonant quasi-energy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator. Interestingly, the effects of disorder are not necessarily adverse: we show that in the same quantum well, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). We identify the conditions on the driving field necessary for observing such a transition.

%B Physical Review B %V 96 %P 054207 %8 2017/08/16 %G eng %U https://arxiv.org/abs/1702.02956 %N 5 %R 10.1103/PhysRevB.96.054207 %0 Journal Article %J Physical Review A %D 2017 %T Dispersive optical detection of magnetic Feshbach resonances in ultracold gases %A Bianca J. Sawyer %A Milena S. J. Horvath %A Eite Tiesinga %A Amita B. Deb %A Niels Kjærgaard %XMagnetically tunable Feshbach resonances in ultracold atomic systems are chiefly identified and characterized through time consuming atom loss spectroscopy. We describe an off-resonant dispersive optical probing technique to rapidly locate Feshbach resonances and demonstrate the method by locating four resonances of

We provide results for the exponential dominating numbers and total exponential dominating numbers of a family of triangular grid graphs. We then prove inequalities for these numbers and compare them with inequalities that hold more generally for exponential dominating numbers of graphs.

%B Involve, a Journal of Mathematics %V 10 %P 749 - 766 %8 2017/05/14 %G eng %U http://msp.org/involve/http://msp.org/involve/2017/10-5/index.xhtmlhttp://msp.org/involve/2017/10-5/p03.xhtmlhttp://msp.org/involve/2017/10-5/involve-v10-n5-p03-s.pdf %N 5 %! Involve %R 10.2140/involve10.2140/involve.2017.10-510.2140/involve.2017.10.749 %0 Journal Article %J Nature Communications %D 2017 %T Dynamically induced robust phonon transport and chiral cooling in an optomechanical system %A Seunghwi Kim %A Xunnong Xu %A Jacob M. Taylor %A Gaurav Bahl %XThe transport of sound and heat, in the form of phonons, has a fundamental material limit: disorder-induced scattering. In electronic and optical settings, introduction of chiral transport - in which carrier propagation exhibits broken parity symmetry - provides robustness against such disorder by preventing elastic backscattering. Here we experimentally demonstrate a path for achieving robust phonon transport even in the presence of material disorder, by dynamically inducing chirality through traveling-wave optomechanical coupling. Using this approach, we demonstrate dramatic optically-induced chiral transport for clockwise and counterclockwise phonons in a symmetric resonator. This induced chirality also enhances isolation from the thermal bath and leads to gain-free reduction of the intrinsic damping of the phonons. Surprisingly, this passive mechanism is also accompanied by a chiral reduction in heat load leading to a novel optical cooling of the mechanics. This technique has the potential to improve upon the fundamental thermal limits of resonant mechanical sensor, which cannot be otherwise attained through conventional optomechanical cooling.

%B Nature Communications %V 8 %P 205 %8 2017/06/19 %G eng %U https://arxiv.org/abs/1609.08674 %R 10.1038/s41467-017-00247-7 %0 Journal Article %J Physical Review Letters %D 2017 %T Entanglement area laws for long-range interacting systems %A Zhe-Xuan Gong %A Michael Foss-Feig %A Fernando G. S. L. Brandão %A Alexey V. Gorshkov %XWe prove that the entanglement entropy of any state evolved under an arbitrary 1/rα long-range-interacting D-dimensional lattice spin Hamiltonian cannot change faster than a rate proportional to the boundary area for any α > D + 1. We also prove that for any α > 2D + 2, the ground state of such a Hamiltonian satisfies the entanglement area law if it can be transformed along a gapped adiabatic path into a ground state known to satisfy the area law. These results significantly generalize their existing counterparts for short-range interacting systems, and are useful for identifying dynamical phase transitions and quantum phase transitions in the presence of long-range interactions.

%B Physical Review Letters %V 119 %P 050501 %8 2017/07/31 %G eng %U https://arxiv.org/abs/1702.05368 %N 5 %R 10.1103/PhysRevLett.119.050501 %0 Journal Article %J Quantum Information & Computation %D 2017 %T Efficient quantum algorithms for analyzing large sparse electrical networks %A Guoming Wang %XAnalyzing large sparse electrical networks is a fundamental task in physics, electrical engineering and computer science. We propose two classes of quantum algorithms for this task. The first class is based on solving linear systems, and the second class is based on using quantum walks. These algorithms compute various electrical quantities, including voltages, currents, dissipated powers and effective resistances, in time poly(d, c,log(N),1/λ,1/ε), where N is the number of vertices in the network, d is the maximum unweighted degree of the vertices, c is the ratio of largest to smallest edge resistance, λ is the spectral gap of the normalized Laplacian of the network, and ε is the accuracy. Furthermore, we show that the polynomial dependence on 1/λ is necessary. This implies that our algorithms are optimal up to polynomial factors and cannot be signficantly improved.

%B Quantum Information & Computation %V 17 %P 987-1026 %8 2017/07/21 %G eng %U https://arxiv.org/abs/1311.1851 %N 11&12 %0 Journal Article %J Quantum Information and Computation %D 2017 %T Efficient simulation of sparse Markovian quantum dynamics %A Andrew M. Childs %A Tongyang Li %XQuantum algorithms for simulating Hamiltonian dynamics have been extensively developed, but there has been much less work on quantum algorithms for simulating the dynamics of open quantum systems. We give the first efficient quantum algorithms for simulating Markovian quantum dynamics generated by Lindbladians that are not necessarily local. We introduce two approaches to simulating sparse Lindbladians. First, we show how to simulate Lindbladians that act within small invariant subspaces using a quantum algorithm to implement sparse Stinespring isometries. Second, we develop a method for simulating sparse Lindblad operators by concatenating a sequence of short-time evolutions. We also show limitations on Lindbladian simulation by proving a no-fast-forwarding theorem for simulating sparse Lindbladians in a black-box model.

%B Quantum Information and Computation %V 17 %P 901-947 %8 2017/09/01 %G eng %U https://arxiv.org/abs/1611.05543 %R 10.26421/QIC17.11-12 %0 Journal Article %J Physical Review Letters %D 2017 %T Efimov States of Strongly Interacting Photons %A M. J. Gullans %A S. Diehl %A S. T. Rittenhouse %A B. P. Ruzic %A J. P. D'Incao %A P. Julienne %A Alexey V. Gorshkov %A J. M. Taylor %XWe demonstrate the emergence of universal Efimov physics for interacting photons in cold gases of Rydberg atoms. We consider the behavior of three photons injected into the gas in their propagating frame, where a paraxial approximation allows us to consider them as massive particles. In contrast to atoms and nuclei, the photons have a large anisotropy between their longitudinal mass, arising from dispersion, and their transverse mass, arising from diffraction. Nevertheless, we show that in suitably rescaled coordinates the effective interactions become dominated by s-wave scattering near threshold and, as a result, give rise to an Efimov effect near unitarity, but with spatially anisotropic wavefunctions in the original coordinates. We show that the three-body loss of these Efimov trimers can be strongly suppressed and determine conditions under which these states are observable in current experiments. These effects can be naturally extended to probe few-body universality beyond three bodies, as well as the role of Efimov physics in the non-equilbrium, many-body regime.

%B Physical Review Letters %V 119 %P 233601 %8 2017/12/04 %G eng %U https://arxiv.org/abs/1709.01955 %N 23 %R 10.1103/PhysRevLett.119.233601 %0 Journal Article %D 2017 %T An Elementary Proof of Private Random Number Generation from Bell Inequalities %A Carl A. Miller %XThe field of device-independent quantum cryptography has seen enormous success in the past several years, including security proofs for key distribution and random number generation that account for arbitrary imperfections in the devices used. Full security proofs in the field so far are long and technically deep. In this paper we show that the concept of the mirror adversary can be used to simplify device-independent proofs. We give a short proof that any bipartite Bell violation can be used to generate private random numbers. The proof is based on elementary techniques and is self-contained.

%8 2017/07/20 %G eng %U https://arxiv.org/abs/1707.06597 %0 Journal Article %J Physical Review A %D 2017 %T Emergent equilibrium in many-body optical bistability %A Michael Foss-Feig %A Pradeep Niroula %A Jeremy T. Young %A Mohammad Hafezi %A Alexey V. Gorshkov %A Ryan M. Wilson %A Mohammad F. Maghrebi %XMany-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.

%B Physical Review A %V 95 %P 043826 %8 2017/04/17 %G eng %U https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.043826 %R doi.org/10.1103/PhysRevA.95.043826 %0 Journal Article %D 2017 %T Entanglement Wedge Reconstruction via Universal Recovery Channels %A Jordan Cotler %A Patrick Hayden %A Geoffrey Penington %A Grant Salton %A Brian Swingle %A Michael Walter %XWe apply and extend the theory of universal recovery channels from quantum information theory to address the problem of entanglement wedge reconstruction in AdS/CFT. It has recently been proposed that any low-energy local bulk operators in a CFT boundary region's entanglement wedge can be reconstructed on that boundary region itself. Existing work arguing for this proposal relies on algebraic consequences of the exact equivalence between bulk and boundary relative entropies, namely the theory of operator algebra quantum error correction. However, bulk and boundary relative entropies are only approximately equal in bulk effective field theory, and in similar situations it is known that predictions from exact entropic equalities can be qualitatively incorrect. The framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture in addition to new physical insights. Most notably, we find that a bulk operator acting in a given boundary region's entanglement wedge can be expressed as the response of the boundary region's modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator. This formula can be interpreted as a noncommutative version of Bayes' rule that attempts to undo the noise induced by restricting to only a portion of the boundary, and has an integral representation in terms of modular flows. To reach these conclusions, we extend the theory of universal recovery channels to finite-dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra

%G eng %U https://arxiv.org/abs/1704.05839 %0 Journal Article %J Physical Review A %D 2017 %T Exact sampling hardness of Ising spin models %A Bill Fefferman %A Michael Foss-Feig %A Alexey V. Gorshkov %XWe study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of *exact* classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in *Proceedings of the 31st Conference on Computational Complexity (CCC 2016)*, Leibniz International Proceedings in Informatics (Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as "boundary degeneracy") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.

%B Physical Review B %V 95 %8 2017/01/25 %G eng %U http://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.045309 %& 045309 %R 10.1103/PhysRevB.95.045309 %0 Conference Proceedings %B Proceedings of the National Academy of Sciences %D 2017 %T Experimental Comparison of Two Quantum Computing Architectures %A N.M. Linke %A Dmitri Maslov %A Martin Roetteler %A S. Debnath %A C. Figgatt %A K. A. Landsman %A K. Wright %A Christopher Monroe %XWe run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device [1] with limited connectivity, and the other is a fully connected trapped-ion system [2]. Even though the two systems have different native quantum interactions, both can be programmed in a way that is blind to the underlying hardware, thus allowing the first comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that employ more connectivity clearly benefit from a better connected system of qubits. While the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that co-designing particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.

%B Proceedings of the National Academy of Sciences %7 13 %V 114 %P 3305-3310 %8 2017/03/21 %G eng %U http://www.pnas.org/content/114/13/3305 %R 10.1073/pnas.1618020114 %0 Journal Article %J Physical Review Letters %D 2017 %T Experimental demonstration of cheap and accurate phase estimation %A Kenneth Rudinger %A Shelby Kimmel %A Daniel Lobser %A Peter Maunz %XWe demonstrate experimental implementation of robust phase estimation (RPE) to learn the phases of X and Y rotations on a trapped Yb+ ion qubit. We estimate these phases with uncertainties less than 4 · 10−4 radians using as few as 176 total experimental samples per phase, and our estimates exhibit Heisenberg scaling. Unlike standard phase estimation protocols, RPE neither assumes perfect state preparation and measurement, nor requires access to ancillae. We cross-validate the results of RPE with the more resource-intensive protocol of gate set tomography.

%B Physical Review Letters %V 118 %P 190502 %8 2017/05/12 %G eng %U https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.190502 %N 19 %R doi.org/10.1103/PhysRevLett.118.190502 %0 Journal Article %J Physical Review Letters %D 2017 %T Experimental Study of Optimal Measurements for Quantum State Tomography %A Sosa-Martinez, H. %A Lysne, N. K. %A Baldwin, C. H. %A Kalev, A. %A Deutsch, I. H. %A Jessen, P. S. %XQuantum tomography is a critically important tool to evaluate quantum hardware, making it essential to develop optimized measurement strategies that are both accurate and efficient. We compare a variety of strategies using nearly pure test states. Those that are informationally complete for all states are found to be accurate and reliable even in the presence of errors in the measurements themselves, while those designed to be complete only for pure states are far more efficient but highly sensitive to such errors. Our results highlight the unavoidable trade-offs inherent in quantum tomography.

%B Physical Review Letters %V 119 %P 150401 %8 2017/10/13 %G eng %U https://link.aps.org/doi/10.1103/PhysRevLett.119.150401 %N 15 %R 10.1103/PhysRevLett.119.150401 %0 Journal Article %D 2017 %T Experimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling %A Peter Bierhorst %A Emanuel Knill %A Scott Glancy %A Alan Mink %A Stephen P. Jordan %A Andrea Rommal %A Yi-Kai Liu %A Bradley Christensen %A Sae Woo Nam %A Lynden K. Shalm %XRandom numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell test experiment for the generation of randomness that cannot be predicted within any physical theory that allows one to make independent measurement choices and prohibits superluminal signaling. To certify and quantify the randomness, we describe a new protocol that performs well in an experimental regime characterized by low violation of Bell inequalities. Applying an extractor function to our data, we obtained 256 new random bits, uniform to within 0.001.

%8 2017/02/16 %G eng %U https://arxiv.org/abs/1702.05178# %0 Journal Article %D 2017 %T Exponential improvements for quantum-accessible reinforcement learning %A Vedran Dunjko %A Yi-Kai Liu %A Xingyao Wu %A Jacob M. Taylor %XQuantum computers can offer dramatic improvements over classical devices for data analysis tasks such as prediction and classification. However, less is known about the advantages that quantum computers may bring in the setting of reinforcement learning, where learning is achieved via interaction with a task environment. Here, we consider a special case of reinforcement learning, where the task environment allows quantum access. In addition, we impose certain "naturalness" conditions on the task environment, which rule out the kinds of oracle problems that are studied in quantum query complexity (and for which quantum speedups are well-known). Within this framework of quantum-accessible reinforcement learning environments, we demonstrate that quantum agents can achieve exponential improvements in learning efficiency, surpassing previous results that showed only quadratic improvements. A key step in the proof is to construct task environments that encode well-known oracle problems, such as Simon's problem and Recursive Fourier Sampling, while satisfying the above "naturalness" conditions for reinforcement learning. Our results suggest that quantum agents may perform well in certain game-playing scenarios, where the game has recursive structure, and the agent can learn by playing against itself

%G eng %U https://arxiv.org/abs/1710.11160 %0 Journal Article %D 2017 %T Exponential Quantum Speed-ups for Semidefinite Programming with Applications to Quantum Learning %A Fernando G. S. L. Brandão %A Amir Kalev %A Tongyang Li %A Cedric Yen-Yu Lin %A Krysta M. Svore %A Xiaodi Wu %XWe give semidefinite program (SDP) quantum solvers with an exponential speed-up over classical ones. Specifically, we consider SDP instances with m constraint matrices of dimension n, each of rank at most r, and assume that the input matrices of the SDP are given as quantum states (after a suitable normalization). Then we show there is a quantum algorithm that solves the SDP feasibility problem with accuracy ǫ by using √ m log m · poly(log n,r, ǫ −1 ) quantum gates. The dependence on n provides an exponential improvement over the work of Brand ˜ao and Svore [6] and the work of van Apeldoorn et al. [23], and demonstrates an exponential quantum speed-up when m and r are small. We apply the SDP solver to the problem of learning a good description of a quantum state with respect to a set of measurements: Given m measurements and a supply of copies of an unknown state ρ, we show we can find in time √ m log m · poly(log n,r, ǫ −1 ) a description of the state as a quantum circuit preparing a density matrix which has the same expectation values as ρ on the m measurements up to error ǫ. The density matrix obtained is an approximation to the maximum entropy state consistent with the measurement data considered in Jaynes’ principle. As in previous work, we obtain our algorithm by “quantizing” classical SDP solvers based on the matrix multiplicative weight update method. One of our main technical contributions is a quantum Gibbs state sampler for low-rank Hamiltonians with a poly-logarithmic dependence on its dimension based on the techniques developed in quantum principal component analysis, which could be of independent interest. Our quantum SDP solver is different from previous ones in the following two aspects: (1) it follows from a zero-sum game approach of Hazan [11] of solving SDPs rather than the primal-dual approach by Arora and Kale [5]; and (2) it does not rely on any sparsity assumption of the input matrices.

%8 2017/10/06 %G eng %U https://arxiv.org/abs/1710.02581 %0 Journal Article %J Physical Review Letters %D 2017 %T Extracting entanglement geometry from quantum states %A Katharine Hyatt %A James R. Garrison %A Bela Bauer %XTensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network - and hence the geometry - is largely fixed a priori by the choice of tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of non-interacting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.

%B Physical Review Letters %V 119 %8 2017/10/06 %G eng %U https://arxiv.org/abs/1704.01974 %N 14 %R 10.1103/PhysRevLett.119.140502 %0 Journal Article %J Cognitive Neurodynamics %D 2017 %T Extreme learning machines for regression based on V-matrix method %A Yang, Zhiyong %A Zhang, Taohong %A Lu, Jingcheng %A Yuan Su %A Zhang, Dezheng %A Duan, Yaowu %XThis paper studies the joint effect of V-matrix, a recently proposed framework for statistical inferences, and extreme learning machine (ELM) on regression problems. First of all, a novel algorithm is proposed to efficiently evaluate the V-matrix. Secondly, a novel weighted ELM algorithm called V-ELM is proposed based on the explicit kernel mapping of ELM and the V-matrix method. Though V-matrix method could capture the geometrical structure of training data, it tends to assign a higher weight to instance with smaller input value. In order to avoid this bias, a novel method called VI-ELM is proposed by minimizing both the regression error and the V-matrix weighted error simultaneously. Finally, experiment results on 12 real world benchmark datasets show the effectiveness of our proposed methods.

%B Cognitive Neurodynamics %8 2017/06/10 %G eng %U http://dx.doi.org/10.1007/s11571-017-9444-2 %R 10.1007/s11571-017-9444-2 %0 Journal Article %J Physical Review D %D 2017 %T Fast optimization algorithms and the cosmological constant %A Ning Bao %A Raphael Bousso %A Stephen P. Jordan %A Brad Lackey %XDenef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of an NP-hard problem. The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10−120 in a randomly generated 109 -dimensional ADK landscape.

%B Physical Review D %V 96 %P 103512 %8 2017/11/13 %G eng %U https://arxiv.org/abs/1706.08503 %N 10 %R 10.1103/PhysRevD.96.103512 %0 Journal Article %J Physical Review A %D 2017 %T Fast quantum computation at arbitrarily low energy %A Stephen P. Jordan %XOne version of the energy-time uncertainty principle states that the minimum time T⊥ for a quantum system to evolve from a given state to any orthogonal state is h/(4ΔE), where ΔE is the energy uncertainty. A related bound called the Margolus-Levitin theorem states that T⊥≥h/(2⟨E⟩), where ⟨E⟩ is the expectation value of energy and the ground energy is taken to be zero. Many subsequent works have interpreted T⊥ as defining a minimal time for an elementary computational operation and correspondingly a fundamental limit on clock speed determined by a system's energy. Here we present local time-independent Hamiltonians in which computational clock speed becomes arbitrarily large relative to ⟨E⟩ and ΔE as the number of computational steps goes to infinity. We argue that energy considerations alone are not sufficient to obtain an upper bound on computational speed, and that additional physical assumptions such as limits to information density and information transmission speed are necessary to obtain such a bound.

%B Physical Review A %V 95 %P 032305 %8 2017/03/06 %G eng %U http://link.aps.org/doi/10.1103/PhysRevA.95.032305 %R 10.1103/PhysRevA.95.032305 %0 Journal Article %J Physical Review Letters %D 2017 %T Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions %A Zachary Eldredge %A Zhe-Xuan Gong %A Ali Hamed Moosavian %A Michael Foss-Feig %A Alexey V. Gorshkov %XIn short-range interacting systems, the speed at which entanglement can be established between two separated points is limited by a constant Lieb-Robinson velocity. Long-range interacting systems are capable of faster entanglement generation, but the degree of the speed-up possible is an open question. In this paper, we present a protocol capable of transferring a quantum state across a distance

A genuinely N-partite entangled state may display vanishing N-partite correlations measured for arbitrary local observables. In such states the genuine entanglement is noticeable solely in correlations between subsets of particles. A straightforward way to obtain such states for odd N is to design an “antistate” in which all correlations between an odd number of observers are exactly opposite. Evenly mixing a state with its antistate then produces a mixed state with no N-partite correlations, with many of them genuinely multiparty entangled. Intriguingly, all known examples of “entanglement without correlations” involve an *odd* number of particles. Here we further develop the idea of antistates, thereby shedding light on the different properties of even and odd particle systems. We conjecture that there is no antistate to any pure even-N-party entangled state making the simple construction scheme unfeasible. However, as we prove by construction, higher-rank examples of entanglement without correlations for arbitrary even N indeed exist. These classes of states exhibit genuine entanglement and even violate an N-partite Bell inequality, clearly demonstrating the nonclassical features of these states as well as showing their applicability for quantum information processing.

We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631--633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal algorithms for commutator simulation and orthogonality testing, and we give a protocol for creating a coherent superposition of pure states, when given sample access to those states. We also show that this sample-based Hamiltonian simulation can be used as the basis of a universal model of quantum computation that requires only partial swap operations and simple single-qubit states.

Topological states can exhibit electronic coherence on macroscopic length scales. When the coherence length exceeds the wavelength of light, one can expect new phenomena to occur in the optical response of these states. We theoretically characterize this limit for integer quantum Hall states in two-dimensional Dirac materials. We find that the radiation from the bulk is dominated by dipole emission, whose spectral properties vary with the local disorder potential. On the other hand, the radiation from the edge is characterized by large multipole moments in the far-field associated with the efficient transfer of angular momentum from the electrons into the scattered light. These results demonstrate that high-order multipole transitions are a necessary component for the optical spectroscopy and control of quantum Hall and related topological states in electronic systems.

%B Physical Review B %V 95 %P 235439 %8 2017/06/30 %G eng %U https://arxiv.org/abs/1701.03464 %N 23 %R 10.1103/PhysRevB.95.235439 %0 Journal Article %J Physical Review B %D 2017 %T Input-output theory for spin-photon coupling in Si double quantum dots %A Benito, M. %A Mi, X. %A Taylor, J. M. %A Petta, J. R. %A Burkard, Guido %XThe interaction of qubits via microwave frequency photons enables long-distance qubit-qubit coupling and facilitates the realization of a large-scale quantum processor. However, qubits based on electron spins in semiconductor quantum dots have proven challenging to couple to microwave photons. In this theoretical work we show that a sizable coupling for a single electron spin is possible via spin-charge hybridization using a magnetic field gradient in a silicon double quantum dot. Based on parameters already shown in recent experiments, we predict optimal working points to achieve a coherent spin-photon coupling, an essential ingredient for the generation of long-range entanglement. Furthermore, we employ input-output theory to identify observable signatures of spin-photon coupling in the cavity output field, which may provide guidance to the experimental search for strong coupling in such spin-photon systems and opens the way to cavity-based readout of the spin qubit.

%B Physical Review B %V 96 %P 235434 %8 2017/12/22 %G eng %U https://link.aps.org/doi/10.1103/PhysRevB.96.235434 %N 23 %R 10.1103/PhysRevB.96.235434 %0 Journal Article %J Phys. Rev. A 96, 052334 %D 2017 %T Lieb-Robinson bounds on n-partite connected correlation functions %A Minh Cong Tran %A James R. Garrison %A Zhe-Xuan Gong %A Alexey V. Gorshkov %XLieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

%B Phys. Rev. A 96, 052334 %G eng %U https://arxiv.org/abs/1705.04355 %R https://doi.org/10.1103/PhysRevA.96.052334 %0 Journal Article %J Physical Review A %D 2017 %T Lieb-Robinson bounds on n-partite connected correlations %A Minh Cong Tran %A James R. Garrison %A Zhe-Xuan Gong %A Alexey V. Gorshkov %XLieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at non-zero relative angular momentum can become dominant, resembling a hollow-core pseudo-potential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν = 1/2 and ν = 2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

%B Physical Review Letters %V 119 %P 247403 %8 2017/12/15 %G eng %U https://arxiv.org/abs/1612.08748 %N 24 %R 10.1103/PhysRevLett.119.247403 %0 Journal Article %D 2017 %T Machine Learning techniques for state recognition and auto-tuning in quantum dots %A Sandesh S. Kalantre %A Justyna P. Zwolak %A Stephen Ragole %A Xingyao Wu %A Neil M. Zimmerman %A M. D. Stewart %A Jacob M. Taylor %XRecent progress in building large-scale quantum devices for exploring quantum computing and simulation paradigms has relied upon effective tools for achieving and maintaining good experimental parameters, i.e. tuning up devices. In many cases, including in quantum-dot based architectures, the parameter space grows substantially with the number of qubits, and may become a limit to scalability. Fortunately, machine learning techniques for pattern recognition and image classification using so-called deep neural networks have shown surprising successes for computer-aided understanding of complex systems. In this work, we use deep and convolutional neural networks to characterize states and charge configurations of semiconductor quantum dot arrays when one can only measure a current-voltage characteristic of transport (here conductance) through such a device. For simplicity, we model a semiconductor nanowire connected to leads and capacitively coupled to depletion gates using the Thomas-Fermi approximation and Coulomb blockade physics. We then generate labeled training data for the neural networks, and find at least 90 % accuracy for charge and state identification for single and double dots purely from the dependence of the nanowire’s conductance upon gate voltages. Using these characterization networks, we can then optimize the parameter space to achieve a desired configuration of the array, a technique we call ‘auto-tuning’. Finally, we show how such techniques can be implemented in an experimental setting by applying our approach to an experimental data set, and outline further problems in this domain, from using charge sensing data to extensions to full one and two-dimensional arrays, that can be tackled with machine learning.

%8 2017/12/13 %G eng %U https://arxiv.org/abs/1712.04914 %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2017 %T Modulus of continuity eigenvalue bounds for homogeneous graphs and convex subgraphs with applications to quantum Hamiltonians %A Michael Jarret %A Stephen P. Jordan %XWe adapt modulus of continuity estimates to the study of spectra of combinatorial graph Laplacians, as well as the Dirichlet spectra of certain weighted Laplacians. The latter case is equivalent to stoquastic Hamiltonians and is of current interest in both condensed matter physics and quantum computing. In particular, we introduce a new technique which bounds the spectral gap of such Laplacians (Hamiltonians) by studying the limiting behavior of the oscillations of their eigenvectors when introduced into the heat equation. Our approach is based on recent advances in the PDE literature, which include a proof of the fundamental gap theorem by Andrews and Clutterbuck.

%B Journal of Mathematical Analysis and Applications %V 452 %P 1269-1290 %8 2017/03/03 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022247X1730272X %N 2 %R 10.1016/j.jmaa.2017.03.030 %0 Journal Article %J Physical Review A %D 2017 %T Multicritical behavior in dissipative Ising models %A Vincent R. Overbeck %A Mohammad F. Maghrebi %A Alexey V. Gorshkov %A Hendrik Weimer %XWe analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.

%B Physical Review A %V 95 %P 042133 %8 2017/04/26 %G eng %U https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.042133 %R doi.org/10.1103/PhysRevA.95.042133 %0 Journal Article %D 2017 %T Nonlocal games, synchronous correlations, and Bell inequalities %A Brad Lackey %A Nishant Rodrigues %XA nonlocal game with a synchronous correlation is a natural generalization of a function between two finite sets, and has recently appeared in the context of quantum graph homomorphisms. In this work we examine analogues of Bell's inequalities for synchronous correlations. We show that, unlike general correlations and the CHSH inequality, there can be no quantum Bell violation among synchronous correlations with two measurement settings. However we exhibit explicit analogues of Bell's inequalities for synchronous correlations with three measurement settings and two outputs, provide an analogue of Tsirl'son's bound in this setting, and give explicit quantum correlations that saturate this bound.

%8 2017/09/21 %G eng %U https://arxiv.org/abs/1707.06200 %0 Journal Article %J Nature %D 2017 %T Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator %A J. Zhang %A G. Pagano %A P. W. Hess %A A. Kyprianidis %A P. Becker %A H. Kaplan %A Alexey V. Gorshkov %A Z. -X. Gong %A C. Monroe %XA quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of qubits, the simulator can tackle a wider range of problems, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. We use a quantum simulator composed of up to 53 qubits to study a non-equilibrium phase transition in the transverse field Ising model of magnetism, in a regime where conventional statistical mechanics does not apply. The qubits are represented by trapped ion spins that can be prepared in a variety of initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with near 99% efficiency. This allows the single-shot measurement of arbitrary many-body correlations for the direct probing of the dynamical phase transition and the uncovering of computationally intractable features that rely on the long-range interactions and high connectivity between the qubits.

%B Nature %V 551 %P 601-604 %8 2017/11/29 %G eng %U https://www.nature.com/articles/nature24654 %R 10.1038/nature24654 %0 Journal Article %J Quantum Information Processing %D 2017 %T Optimal length of decomposition sequences composed of imperfect gates %A Yunseong Nam %A R. Blümel %XQuantum error correcting circuitry is both a resource for correcting errors and a source for generating errors. A balance has to be struck between these two aspects. Perfect quantum gates do not exist in nature. Therefore, it is important to investigate how flaws in the quantum hardware affect quantum computing performance. We do this in two steps. First, in the presence of realistic, faulty quantum hardware, we establish how quantum error correction circuitry achieves reduction in the extent of quantum information corruption. Then, we investigate fault-tolerant gate sequence techniques that result in an approximate phase rotation gate, and establish the existence of an optimal length of the length *L* of the decomposition sequence. The existence of is due to the competition between the increase in gate accuracy with increasing *L*, but the decrease in gate performance due to the diffusive proliferation of gate errors due to faulty basis gates. We present an analytical formula for the gate fidelity as a function of *L* that is in satisfactory agreement with the results of our simulations and allows the determination of via the solution of a transcendental equation. Our result is universally applicable since gate sequence approximations also play an important role, e.g., in atomic and molecular physics and in nuclear magnetic resonance.

The simplest cosmologyâ€”the Friedmannâ€“Robertsonâ€“Walkerâ€“LemaÃ®tre (FRW) modelâ€” describes a spatially homogeneous and isotropic universe where the scale factor is the only dynamical parameter. Here we consider how quantized electromagnetic fields become entangled with the scale factor in a toy version of the FRW model. A system consisting of a photon, source, and detector is described in such a universe, and we find that the detection of a redshifted photon by the detector system constrains possible scale factor superpositions. Thus, measuring the redshift of the photon is equivalent to a weak measurement of the underlying cosmology. We also consider a potential optomechanical analogy system that would enable experimental exploration of these concepts. The analogy focuses on the effects of photon redshift measurement as a quantum back-action on metric variables, where the position of a movable mirror plays the role of the scale factor. By working in the rotating frame, an effective Hubble equation can be simulated with a simple free moving mirror.

%B Entropy %V 19 %8 2017/09/12 %G eng %U http://www.mdpi.com/1099-4300/19/9/485 %N 9 %& 485 %R 10.3390/e19090485 %0 Journal Article %D 2017 %T Optomechanically-induced chiral transport of phonons in one dimension %A Xunnong Xu %A Jacob M. Taylor %XNon-reciprocal devices, with one-way transport properties, form a key component for isolating and controlling light in photonic systems. Optomechanical systems have emerged as a potential platform for optical non-reciprocity, due to ability of a pump laser to break time and parity symmetry in the system. Here we consider how the non-reciprocal behavior of light can also impact the transport of sound in optomechanical devices. We focus on the case of a quasi one dimensional optical ring resonator with many mechanical modes coupled to light via the acousto-optic effect. The addition of disorder leads to finite diffusion for phonon transport in the material, largely due to elastic backscattering between clockwise and counter-clockwise phonons. We show that a laser pump field, along with the assumption of high quality-factor, sideband-resolved optical resonances, suppresses the effects of disorder and leads to the emergence of chiral diffusion, with direction-dependent diffusion emerging in a bandwidth similar to the phase-matching bandwidth for Brillouin scattering. A simple diagrammatic theory connects the observation of reduced mechanical linewidths directly to the associated phonon diffusion properties, and helps explain recent experimental results.

%8 2017/01/10 %G eng %U https://arxiv.org/abs/1701.02699 %0 Journal Article %D 2017 %T Out-of-time-order correlators in finite open systems %A S. V. Syzranov %A Alexey V. Gorshkov %A V. Galitski %XWe study out-of-time order correlators (OTOCs) of the form hAˆ(t)Bˆ(0)Cˆ(t)Dˆ(0)i for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small region in a disordered interacting medium coupled to the rest of this medium considered as an environment. We demonstrate that for a system with discrete energy levels the OTOC saturates exponentially ∝ Paie −t/τi + const to a constant value at t → ∞, in contrast with quantum-chaotic systems which exhibit exponential growth of OTOCs. Focussing on the case of a two-level system, we calculate microscopically the decay times τi and the value of the saturation constant. Because some OTOCs are immune to dephasing processes and some are not, such correlators may decay on two sets of parametrically different time scales related to inelastic transitions between the system levels and to pure dephasing processes, respectively. In the case of a classical environment, the evolution of the OTOC can be mapped onto the evolution of the density matrix of two systems coupled to the same dissipative environment.

%8 2017/04/27 %G eng %U https://arxiv.org/abs/1704.08442 %R https://doi.org/10.1103/PhysRevB.97.161114 %0 Journal Article %D 2017 %T Parallel Device-Independent Quantum Key Distribution %A Rahul Jain %A Carl Miller %A Yaoyun Shi %XA prominent application of quantum cryptography is the distribution of cryptographic keys with unconditional security. Recently, such security was extended by Vazirani and Vidick (Physical Review Letters, 113, 140501, 2014) to the device-independent (DI) scenario, where the users do not need to trust the integrity of the underlying quantum devices. The protocols analyzed by them and by subsequent authors all require a sequential execution of N multiplayer games, where N is the security parameter. In this work, we prove unconditional security of a protocol where all games are executed in parallel. Our result further reduces the requirements for QKD (allowing for arbitrary information leakage within each players' lab) and opens the door to more efficient implementation. To the best of our knowledge, this is the first parallel security proof for a fully device-independent QKD protocol. Our protocol tolerates a constant level of device imprecision and achieves a linear key rate.

%8 2017/03/15 %G eng %U https://arxiv.org/abs/1703.05426 %0 Journal Article %J Physical Review B %D 2017 %T Partial breakdown of quantum thermalization in a Hubbard-like model %A James R. Garrison %A Ryan V. Mishmash %A Matthew P. A. Fisher %XWe study the possible breakdown of quantum thermalization in a model of itinerant electrons on a one-dimensional chain without disorder, with both spin and charge degrees of freedom. The eigenstates of this model exhibit peculiar properties in the entanglement entropy, the apparent scaling of which is modified from a “volume law” to an “area law” after performing a partial, site-wise measurement on the system. These properties and others suggest that this model realizes a new, nonthermal phase of matter, known as a quantum disentangled liquid (QDL). The putative existence of this phase has striking implications for the foundations of quantum statistical mechanics.

%B Physical Review B %V 95 %P 054204 %8 2017/02/17 %G eng %U http://link.aps.org/doi/10.1103/PhysRevB.95.054204 %R 10.1103/PhysRevB.95.054204 %0 Journal Article %D 2017 %T Penalty models for bitstrings of constant Hamming weight %A Brad Lackey %XTo program a quantum annealer, one must construct objective functions whose minima encode hard constraints imposed by the underlying problem. For such "penalty models," one desires the additional property that the gap in the objective value between such minima and states that fail the constraints is maximized amongst the allowable objective functions. In this short note, we prove the standard penalty model for the constraint that a bitstring has given Hamming weight is optimal with respect to objective value gap.

%8 2017/04/24 %G eng %U https://arxiv.org/abs/1704.07290 %0 Journal Article %J Physical Review A %D 2017 %T Pendular trapping conditions for ultracold polar molecules enforced by external electric fields %A Ming Li %A Alexander Petrov %A Constantinos Makrides %A Eite Tiesinga %A Svetlanta Kotochigova %XWe theoretically investigate trapping conditions for ultracold polar molecules in optical lattices, when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar

We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |tr(C†U)|2 with unitary matrices C that are chosen by the observer. This problem has applications to quantum process tomography, when the unknown process is a unitary operation. We show that PhaseLift, a convex programming algorithm for phase retrieval, can be adapted to this matrix setting, using measurements that are sampled from unitary 4- and 2-designs. In the case of unitary 4-design measurements, we show that PhaseLift can reconstruct all unitary matrices, using a nearoptimal number of measurements. This extends previous work on PhaseLift using spherical 4-designs. In the case of unitary 2-design measurements, we show that PhaseLift still works pretty well on average: it recovers almost all signals, up to a constant additive error, using a near-optimal number of measurements. These 2-design measurements are convenient for quantum process tomography, as they can be implemented via randomized benchmarking techniques. This is the first positive result on PhaseLift using 2-designs.

%B SampTA 2017 %8 2017/07 %G eng %U http://ieeexplore.ieee.org/document/8024414/ %R 10.1109/SAMPTA.2017.8024414 %0 Journal Article %J Physical Review A %D 2017 %T Phase-space mixing in dynamically unstable, integrable few-mode quantum systems %A Ranchu Mathew %A Eite Tiesinga %XQuenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA) and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as 1/O(ln N), where N is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady state value is a damped oscillation and the damping is Gaussian in time. We confirm our results with numerical TWA simulations.

%B Physical Review A %V 96 %P 013604 %8 2017/07/05 %G eng %U https://arxiv.org/abs/1705.01702 %N 1 %R 10.1103/PhysRevA.96.013604 %0 Journal Article %D 2017 %T Provable quantum state tomography via non-convex methods %A Anastasios Kyrillidis %A Amir Kalev %A Dohuyng Park %A Srinadh Bhojanapalli %A Constantine Caramanis %A Sujay Sanghavi %XWith nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from non-convex optimization. The algorithm excels in the compressed-sensing-like setting, where only a few data points are measured from a lowrank or highly-pure quantum state of a high-dimensional system. We show that the algorithm can practically be used in quantum tomography problems that are beyond the reach of convex solvers, and, moreover, is faster than other state-of-the-art non-convex approaches. Crucially, we prove that, despite being a non-convex program, under mild conditions, the algorithm is guaranteed to converge to the global minimum of the problem; thus, it constitutes a provable quantum state tomography protocol.

%8 2017/11/19 %G eng %U https://arxiv.org/abs/1711.02524 %0 Journal Article %J Communications in Mathematical Physics %D 2017 %T Quantum algorithm for linear differential equations with exponentially improved dependence on precision %A Dominic W. Berry %A Andrew M. Childs %A Aaron Ostrander %A Guoming Wang %XWe present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time. The complexity of the algorithm is polynomial in the logarithm of the inverse error, an exponential improvement over previous quantum algorithms for this problem. Our result builds upon recent advances in quantum linear systems algorithms by encoding the simulation into a sparse, well-conditioned linear system that approximates evolution according to the propagator using a Taylor series. Unlike with finite difference methods, our approach does not require additional hypotheses to ensure numerical stability.

%B Communications in Mathematical Physics %V 356 %P 1057-1081 %8 2017/12/01 %G eng %U https://arxiv.org/abs/1701.03684 %N 3 %0 Journal Article %J Physical Review A %D 2017 %T Quantum Algorithm for Linear Regression %A Guoming Wang %XWe present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which only yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at negligible cost. Moreover, our algorithm does not require the design matrix to be sparse or need any help from additional state preparation procedures. It runs in time poly(log(N), d, κ, 1/), where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit without computing its parameters explicitly. This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

%B Physical Review A %V 96 %P 012335 %8 2017/07/31 %G eng %U https://arxiv.org/abs/1402.0660 %0 Journal Article %J SIAM Journal on Computing %D 2017 %T Quantum algorithm for systems of linear equations with exponentially improved dependence on precision %A Andrew M. Childs %A Robin Kothari %A Rolando D. Somma %XHarrow, Hassidim, and Lloyd showed that for a suitably specified N×N matrix A and N-dimensional vector b⃗ , there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of equations Ax⃗ =b⃗ . If A is sparse and well-conditioned, their algorithm runs in time poly(logN,1/ϵ), where ϵ is the desired precision in the output state. We improve this to an algorithm whose running time is polynomial in log(1/ϵ), exponentially improving the dependence on precision while keeping essentially the same dependence on other parameters. Our algorithm is based on a general technique for implementing any operator with a suitable Fourier or Chebyshev series representation. This allows us to bypass the quantum phase estimation algorithm, whose dependence on ϵ is prohibitive.

%B SIAM Journal on Computing %V 46 %P 1920-1950 %8 2017/12/21 %G eng %U http://epubs.siam.org/doi/10.1137/16M1087072 %N 6 %R 10.1137/16M1087072 %0 Journal Article %D 2017 %T Quantum Algorithms for Graph Connectivity and Formula Evaluation %A Stacey Jeffery %A Shelby Kimmel %XWe give a new upper bound on the quantum query complexity of deciding st-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation reduces to deciding connectivity on just such a class of graphs. Applying the algorithm for st-connectivity to Boolean formula evaluation problems, we match the O( √ N) bound on the quantum query complexity of evaluating formulas on N variables, give a quadratic speed-up over the classical query complexity of a certain class of promise Boolean formulas, and show this approach can yield superpolynomial quantum/classical separations. These results indicate that this st-connectivity-based approach may be the “right” way of looking at quantum algorithms for formula evaluation.

%8 2017/04/03 %G eng %U https://arxiv.org/abs/1704.00765 %0 Journal Article %J Proceedings of ASIACRYPT 2017 %D 2017 %T Quantum Fully Homomorphic Encryption With Verification %A Gorjan Alagic %A Yfke Dulek %A Christian Schaffner %A Florian Speelman %XFully-homomorphic encryption (FHE) enables computation on encrypted data while maintaining secrecy. Recent research has shown that such schemes exist even for quantum computation. Given the numerous applications of classical FHE (zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is reasonable to hope that quantum FHE (or QFHE) will lead to many new results in the quantum setting. However, a crucial ingredient in almost all applications of FHE is circuit verification. Classically, verification is performed by checking a transcript of the homomorphic computation. Quantumly, this strategy is impossible due to no-cloning. This leads to an important open question: can quantum computations be delegated and verified in a non-interactive manner? In this work, we answer this question in the affirmative, by constructing a scheme for QFHE with verification (vQFHE). Our scheme provides authenticated encryption, and enables arbitrary polynomial-time quantum computations without the need of interaction between client and server. Verification is almost entirely classical; for computations that start and end with classical states, it is completely classical. As a first application, we show how to construct quantum one-time programs from classical one-time programs and vQFHE.

%B Proceedings of ASIACRYPT 2017 %P 438-467 %8 2017/11/30 %G eng %U https://arxiv.org/abs/1708.09156 %R 10.1007/978-3-319-70694-8_16 %0 Journal Article %D 2017 %T Quantum query complexity of entropy estimation %A Tongyang Li %A Xiaodi Wu %XEstimation of Shannon and R´enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on the number of samples to estimate these entropies have been established in the classical setting, while little is known about their quantum counterparts. In this paper, we give the first quantum algorithms for estimating α- R´enyi entropies (Shannon entropy being 1-Renyi entropy). In particular, we demonstrate a quadratic quantum speedup for Shannon entropy estimation and a generic quantum speedup for α-R´enyi entropy estimation for all α ≥ 0, including a tight bound for the collision-entropy (2-R´enyi entropy). We also provide quantum upper bounds for extreme cases such as the Hartley entropy (i.e., the logarithm of the support size of a distribution, corresponding to α = 0) and the min-entropy case (i.e., α = +∞), as well as the Kullback-Leibler divergence between two distributions. Moreover, we complement our results with quantum lower bounds on α-R´enyi entropy estimation for all α ≥ 0. Our approach is inspired by the pioneering work of Bravyi, Harrow, and Hassidim (BHH) [13] on quantum algorithms for distributional property testing, however, with many new technical ingredients. For Shannon entropy and 0-R´enyi entropy estimation, we improve the performance of the BHH framework, especially its error dependence, using Montanaro’s approach to estimating the expected output value of a quantum subroutine with bounded variance [41] and giving a fine-tuned error analysis. For general α-R´enyi entropy estimation, we further develop a procedure that recursively approximates α-R´enyi entropy for a sequence of αs, which is in spirit similar to a cooling schedule in simulated annealing. For special cases such as integer α ≥ 2 and α = +∞ (i.e., the min-entropy), we reduce the entropy estimation problem to the α-distinctness and the dlog ne-distinctness problems, respectively. We exploit various techniques to obtain our lower bounds for different ranges of α, including reductions to (variants of) existing lower bounds in quantum query complexity as well as the polynomial method inspired by the celebrated quantum lower bound for the collision problem.

%8 2017/10/16 %G eng %U https://arxiv.org/abs/1710.06025 %0 Journal Article %D 2017 %T Quantum simulation of ferromagnetic Heisenberg model %A Yiping Wang %A Minh Cong Tran %A Jacob M. Taylor %XLarge quantum simulators, with sufficiently many qubits to be impossible to simulate classically, become hard to experimentally validate. We propose two tests of a quantum simulator with Heisenberg interaction in a linear chain of spins. In the first, we propagate half of a singlet state through a chain of spin with a ferromagnetic interaction and subsequently recover the state with an antiferromagnetic interaction. The antiferromagnetic interaction is intrinsic to the system while the ferromagnetic one can be simulated by a sequence of time-dependent controls of the antiferromagnetic interaction and Suzuki-Trotter approximations. In the second test, we use the same technique to transfer a spin singlet state from one end of a spin chain to the other. We show that the tests are robust against parametric errors in operation of the simulator and may be applicable even without error correction.

%8 2017/12/14 %G eng %U https://arxiv.org/abs/1712.05282 %0 Journal Article %J Physical Review Letters %D 2017 %T Quantum state tomography via reduced density matrices %A Tao Xin %A Dawei Lu %A Joel Klassen %A Nengkun Yu %A Zhengfeng Ji %A Jianxin Chen %A Xian Ma %A Guilu Long %A Bei Zeng %A Raymond Laflamme %XQuantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results advance the project of performing efficient and accurate quantum state tomography in practice.

%B Physical Review Letters %V 118 %P 020401 %8 2017/01/09 %G eng %U http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.020401 %R 10.1103/PhysRevLett.118.020401 %0 Journal Article %J Quantum Information and Computation %D 2017 %T Randomness in nonlocal games between mistrustful players %A Carl Miller %A Yaoyun Shi %XIf two quantum players at a nonlocal game G achieve a superclassical score, then their measurement outcomes must be at least partially random from the perspective of any third player. This is the basis for device-independent quantum cryptography. In this paper we address a related question: does a superclassical score at G guarantee that one player has created randomness from the perspective of the other player? We show that for complete-support games, the answer is yes: even if the second player is given the first player's input at the conclusion of the game, he cannot perfectly recover her output. Thus some amount of local randomness (i.e., randomness possessed by only one player) is always obtained when randomness is certified from nonlocal games with quantum strategies. This is in contrast to non-signaling game strategies, which may produce global randomness without any local randomness. We discuss potential implications for cryptographic protocols between mistrustful parties.

%B Quantum Information and Computation %V 17 %P 0595-0610 %8 2017/06/15 %G eng %U https://arxiv.org/abs/1706.04984 %N 7&8 %0 Journal Article %J Electronic Colloquium on Computational Complexity (ECCC) %D 2017 %T Raz-McKenzie simulation with the inner product gadget %A Xiaodi Wu %A Penghui Yao %A Henry Yuen %XIn this note we show that the Raz-McKenzie simulation algorithm which lifts deterministic query lower bounds to deterministic communication lower bounds can be implemented for functions f composed with the Inner Product gadget 1ip(x, y) = P i xiyi mod 2 of logarithmic size. In other words, given a function f : {0, 1} n → {0, 1} with deterministic query complexity D(f), we show that the deterministic communication complexity of the composed function f ◦ 1 n ip is Θ(D(f) log n), where f ◦ 1 n ip(x, y) = f(1ip(x 1 , y 1 ), . . . , 1ip(x n , y n )) where x = (x 1 , . . . , x n ), y = (y 1 , . . . , y n ) and each x i and y i are O(log n) bit strings. In [RM97] and [GPW15], the simulation algorithm is implemented for functions composed with the Indexing gadget, where the size of the gadget is polynomial in the input length of the outer function f.

%B Electronic Colloquium on Computational Complexity (ECCC) %8 2017/01/28 %G eng %U https://eccc.weizmann.ac.il/report/2017/010/ %0 Journal Article %D 2017 %T On the readiness of quantum optimization machines for industrial applications %A Alejandro Perdomo-Ortiz %A Alexander Feldman %A Asier Ozaeta %A Sergei V. Isakov %A Zheng Zhu %A Bryan O'Gorman %A Helmut G. Katzgraber %A Alexander Diedrich %A Hartmut Neven %A Johan de Kleer %A Brad Lackey %A Rupak Biswas %XThere have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for near-term quantum annealers.

%8 2017/08/31 %G eng %U https://arxiv.org/abs/1708.09780 %0 Journal Article %J Quantum Science and Technology %D 2017 %T Rigidity of the magic pentagram game %A Amir Kalev %A Carl Miller %XA game is rigid if a near-optimal score guarantees, under the sole assumption of the validity of quantum mechanics, that the players are using an approximately unique quantum strategy. Rigidity has a vital role in quantum cryptography as it permits a strictly classical user to trust behavior in the quantum realm. This property can be traced back as far as 1998 (Mayers and Yao) and has been proved for multiple classes of games. In this paper we prove ridigity for the magic pentagram game, a simple binary constraint satisfaction game involving two players, five clauses and ten variables. We show that all near-optimal strategies for the pentagram game are approximately equivalent to a unique strategy involving real Pauli measurements on three maximally-entangled qubit pairs.

%B Quantum Science and Technology %V 3 %P 015002 %8 2017/11/02 %G eng %U http://iopscience.iop.org/article/10.1088/2058-9565/aa931d/meta %N 1 %0 Journal Article %D 2017 %T Robust entanglement renormalization on a noisy quantum computer %A Isaac H. Kim %A Brian Swingle %XA method to study strongly interacting quantum many-body systems at and away from criticality is proposed. The method is based on a MERA-like tensor network that can be efficiently and reliably contracted on a noisy quantum computer using a number of qubits that is much smaller than the system size. We prove that the outcome of the contraction is stable to noise and that the estimated energy upper bounds the ground state energy. The stability, which we numerically substantiate, follows from the positivity of operator scaling dimensions under renormalization group flow. The variational upper bound follows from a particular assignment of physical qubits to different locations of the tensor network plus the assumption that the noise model is local. We postulate a scaling law for how well the tensor network can approximate ground states of lattice regulated conformal field theories in d spatial dimensions and provide evidence for the postulate. Under this postulate, a O(logd (1/δ))-qubit quantum computer can prepare a valid quantum-mechanical state with energy density δ above the ground state. In the presence of noise, δ = O( logd+1(1/)) can be achieved, where is the noise strength.

%8 2017/11/20 %G eng %U https://arxiv.org/abs/1711.07500 %0 Conference Proceedings %B Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) %D 2017 %T Sequential measurements, disturbance and property testing %A Aram W. Harrow %A Cedric Yen-Yu Lin %A Ashley Montanaro %XWe describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and the case that all of the measurements have low probability of acceptance. The measurements cannot simply be tried in sequence, because early measurements may disturb the state being tested. One procedure is based on a variant of Marriott-Watrous amplification. The other procedure is based on the use of a test for this disturbance, which is applied with low probability. We find a number of applications. First, quantum query complexity separations in the property testing model for testing isomorphism of functions under group actions. We give quantum algorithms for testing isomorphism, linear isomorphism and affine isomorphism of boolean functions which use exponentially fewer queries than is possible classically, and a quantum algorithm for testing graph isomorphism which uses polynomially fewer queries than the best algorithm known. Second, testing properties of quantum states and operations. We show that any finite property of quantum states can be tested using a number of copies of the state which is logarithmic in the size of the property, and give a test for genuine multipartite entanglement of states of n qubits that uses O(n) copies of the state. Third, correcting an error in a result of Aaronson on de-Merlinizing quantum protocols. This result claimed that, in any one-way quantum communication protocol where two parties are assisted by an all-powerful but untrusted third party, the third party can be removed with only a modest increase in the communication cost. We give a corrected proof of a key technical lemma required for Aaronson's result.

%B Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) %P 1598-1611 %8 2017/01/01 %G eng %U http://epubs.siam.org/doi/10.1137/1.9781611974782.105 %R 10.1137/1.9781611974782.105 %0 Journal Article %D 2017 %T Shorter stabilizer circuits via Bruhat decomposition and quantum circuit transformations %A Dmitri Maslov %A Martin Roetteler %XIn this paper we improve the layered implementation of arbitrary stabilizer circuits introduced by Aaronson and Gottesman in Phys. Rev. A 70(052328), 2004: to implement a general stabilizer circuit, we reduce their 11-stage computation -HC-P-C-P-C-H-P-C-P-C- over the gate set consisting of Hadamard, Controlled-NOT, and Phase gates, into a 7-stage computation of the form -C-CZ-P-H-P-CZ-C-. We show arguments in support of using -CZ- stages over the -C- stages: not only the use of -CZ- stages allows a shorter layered expression, but -CZ- stages are simpler and appear to be easier to implement compared to the -C- stages. Based on this decomposition, we develop a twoqubit gate depth-(14n−4) implementation of stabilizer circuits over the gate library {H, P, CNOT}, executable in the LNN architecture, improving best previously known depth-25n circuit, also executable in the LNN architecture. Our constructions rely on Bruhat decomposition of the symplectic group and on folding arbitrarily long sequences of the form (-P-C-) m into a 3-stage computation -P-CZ-C-. Our results include the reduction of the 11-stage decomposition -H-C-P-C-P-C-H-P-C-P-C- into a 9-stage decomposition of the form -C-P-C-P-H-C-P-C-P-. This reduction is based on the Bruhat decomposition of the symplectic group. This result also implies a new normal form for stabilizer circuits. We show that a circuit in this normal form is optimal in the number of Hadamard gates used. We also show that the normal form has an asymptotically optimal number of parameters.

%8 2017/05/25 %G eng %U https://arxiv.org/abs/1705.09176 %0 Journal Article %J Physical Review X %D 2017 %T Simultaneous, Full Characterization of a Single-Photon State %A Thomay, Tim %A Polyakov, Sergey V. %A Gazzano, Olivier %A Goldschmidt, Elizabeth %A Eldredge, Zachary D. %A Huber, Tobias %A Loo, Vivien %A Solomon, Glenn S. %XAs single-photon sources become more mature and are used more often in quantum information, communications, and measurement applications, their characterization becomes more important. Singlephoton-like light is often characterized by its brightness, as well as two quantum properties: the suppression of multiphoton content and the photon indistinguishability. While it is desirable to obtain these quantities from a single measurement, currently two or more measurements are required. Here, we show that using two-photon (n ¼ 2) number-resolving detectors, one can completely characterize single-photon-like states in a single measurement, where previously two or more measurements were necessary. We simultaneously determine the brightness, the suppression of multiphoton states, the indistinguishability, and the statistical distribution of Fock states to third order for a quantum light source. We find n ≥ 3 number-resolving detectors provide no additional advantage in the single-photon characterization. The new method extracts more information per experimental trial than a conventional measurement for all input states and is particularly more efficient for statistical mixtures of photon states. Thus, using this n ¼ 2, number-resolving detector scheme will provide advantages in a variety of quantum optics measurements and systems.

%B Physical Review X %V 7 %P 041036 %8 2017/11/15 %G eng %U https://link.aps.org/doi/10.1103/PhysRevX.7.041036 %N 4 %R 10.1103/PhysRevX.7.041036 %0 Journal Article %J Physical Review Letters %D 2017 %T A solvable family of driven-dissipative many-body systems %A Michael Foss-Feig %A Jeremy T. Young %A Victor V. Albert %A Alexey V. Gorshkov %A Mohammad F. Maghrebi %XExactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. And conversely, the relative scarcity of solutions for non-equilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently in any number of spatial dimensions. We leverage these solutions to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions, and to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture.

%B Physical Review Letters %V 119 %8 2017/11/10 %G eng %U https://arxiv.org/abs/1703.04626 %N 19 %R 10.1103/PhysRevLett.119.190402 %0 Journal Article %D 2017 %T Substochastic Monte Carlo Algorithms %A Michael Jarret %A Brad Lackey %XIn this paper we introduce and formalize Substochastic Monte Carlo (SSMC) algorithms. These algorithms, originally intended to be a better classical foil to quantum annealing than simulated annealing, prove to be worthy optimization algorithms in their own right. In SSMC, a population of walkers is initialized according to a known distribution on an arbitrary search space and varied into the solution of some optimization problem of interest. The first argument of this paper shows how an existing classical algorithm, "Go-With-The-Winners" (GWW), is a limiting case of SSMC when restricted to binary search and particular driving dynamics.

Although limiting to GWW, SSMC is more general. We show that (1) GWW can be efficiently simulated within the SSMC framework, (2) SSMC can be exponentially faster than GWW, (3) by naturally incorporating structural information, SSMC can exponentially outperform the quantum algorithm that first inspired it, and (4) SSMC exhibits desirable search features in general spaces. Our approach combines ideas from genetic algorithms (GWW), theoretical probability (Fleming-Viot processes), and quantum computing. Not only do we demonstrate that SSMC is often more efficient than competing algorithms, but we also hope that our results connecting these disciplines will impact each independently. An implemented version of SSMC has previously enjoyed some success as a competitive optimization algorithm for Max-

Recent work on quantum machine learning has demonstrated that quantum computers can offer dramatic improvements over classical devices for data mining, prediction and classification. However, less is known about the advantages using quantum computers may bring in the more general setting of reinforcement learning, where learning is achieved via interaction with a task environment that provides occasional rewards. Reinforcement learning can incorporate data-analysis-oriented learning settings as special cases, but also includes more complex situations where, e.g., reinforcing feedback is delayed. In a few recent works, Grover-type amplification has been utilized to construct quantum agents that achieve up-to-quadratic improvements in learning efficiency. These encouraging results have left open the key question of whether super-polynomial improvements in learning times are possible for genuine reinforcement learning problems, that is problems that go beyond the other more restricted learning paradigms. In this work, we provide a family of such genuine reinforcement learning tasks. We construct quantum-enhanced learners which learn super-polynomially, and even exponentially faster than any classical reinforcement learning model, and we discuss the potential impact our results may have on future technologies.

%8 2017/12/12 %G eng %U https://arxiv.org/abs/1710.11160 %0 Journal Article %D 2017 %T Thermodynamic Analysis of Classical and Quantum Search Algorithms %A Ray Perlner %A Yi-Kai Liu %XWe analyze the performance of classical and quantum search algorithms from a thermodynamic perspective, focusing on resources such as time, energy, and memory size. We consider two examples that are relevant to post-quantum cryptography: Grover’s search algorithm, and the quantum algorithm for collisionfinding. Using Bennett’s “Brownian” model of low-power reversible computation, we show classical algorithms that have the same asymptotic energy consumption as these quantum algorithms. Thus, the quantum advantage in query complexity does not imply a reduction in these thermodynamic resource costs. In addition, we present realistic estimates of the resource costs of quantum and classical search, for near-future computing technologies. We find that, if memory is cheap, classical exhaustive search can be surprisingly competitive with Grover’s algorithm.

%8 2017/09/29 %G eng %U https://arxiv.org/abs/1709.10510 %0 Journal Article %J Physical Review B %D 2017 %T Thermodynamic limits for optomechanical systems with conservative potentials %A Stephen Ragole %A Haitan Xu %A John Lawall %A Jacob M. Taylor %XThe mechanical force from light – radiation pressure – provides an intrinsic nonlinear interaction. Consequently, optomechanical systems near their steady state, such as the canonical optical spring, can display non-analytic behavior as a function of external parameters. This non-analyticity, a key feature of thermodynamic phase transitions, suggests that there could be an effective thermodynamic description of optomechanical systems. Here we explicitly define the thermodynamic limit for optomechanical systems and derive a set of sufficient constraints on the system parameters as the mechanical system grows large. As an example, we show how these constraints can be satisfied in a system with Z2 symmetry and derive a free energy, allowing us to characterize this as an equilibrium phase transition.

%B Physical Review B %V 96 %P 184106 %8 2017/11/13 %G eng %U https://arxiv.org/abs/1707.05771 %N 18 %R 10.1103/PhysRevB.96.184106 %0 Journal Article %J Physical Review Letters %D 2017 %T Threshold Dynamics of a Semiconductor Single Atom Maser %A Liu, Y.-Y. %A Stehlik, J. %A Eichler, C. %A Mi, X. %A Hartke, T. R. %A Gullans, M. J. %A Taylor, J. M. %A Petta, J. R. %XWe demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

%B Physical Review Letters %V 119 %P 097702 %8 2017/08/31 %G eng %U https://link.aps.org/doi/10.1103/PhysRevLett.119.097702 %N 9 %R 10.1103/PhysRevLett.119.097702 %0 Journal Article %D 2017 %T Unforgeable Quantum Encryption %A Gorjan Alagic %A Tommaso Gagliardoni %A Christian Majenz %XWe study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect adversarial cheating in such scenarios. Quantumly, this approach would violate no-cloning. We develop new techniques to overcome this problem: we use entanglement to detect cheating, and rely on recent results for characterizing quantum encryption schemes. We give definitions for (i.) ciphertext unforgeability , (ii.) indistinguishability under adaptive chosen-ciphertext attack, and (iii.) authenticated encryption. The restriction of each definition to the classical setting is at least as strong as the corresponding classical notion: (i) implies INT-CTXT, (ii) implies IND-CCA2, and (iii) implies AE. All of our new notions also imply QIND-CPA privacy. Combining one-time authentication and classical pseudorandomness, we construct schemes for each of these new quantum security notions, and provide several separation examples. Along the way, we also give a new definition of one-time quantum authentication which, unlike all previous approaches, authenticates ciphertexts rather than plaintexts.

%8 2017/09/19 %G eng %U https://arxiv.org/abs/1709.06539 %0 Journal Article %J SIAM Journal on Computing %D 2017 %T Universal Security for Randomness Expansion from the Spot-Checking Protocol %A Carl Miller %A Yaoyun Shi %XColbeck (Thesis, 2006) proposed using Bell inequality violations to generate certified random numbers. While full quantum-security proofs have been given, it remains a major open problem to identify the broadest class of Bell inequalities and lowest performance requirements to achieve such security. In this paper, working within the broad class of spot-checking protocols, we prove exactly which Bell inequality violations can be used to achieve full security. Our result greatly improves the known noise tolerance for secure randomness expansion: for the commonly used CHSH game, full security was only known with a noise tolerance of 1.5%, and we improve this to 10.3%. We also generalize our results beyond Bell inequalities and give the first security proof for randomness expansion based on Kochen-Specker inequalities. The central technical contribution of the paper is a new uncertainty principle for the Schatten norm, which is based on the uniform convexity inequality of Ball, Carlen, and Lieb (Inventiones mathematicae, 115:463-482, 1994).

%B SIAM Journal on Computing %V 46 %8 2017/08/01 %G eng %U http://epubs.siam.org/doi/10.1137/15M1044333 %N 4 %R 10.1137/15M1044333 %0 Journal Article %J New Journal of Physics %D 2017 %T Use of global interactions in efficient quantum circuit constructions %A Dmitri Maslov %A Yunseong Nam %XIn this paper we study the ways to use a global entangling operator to efficiently implement circuitry common to a selection of important quantum algorithms. In particular, we focus on the circuits composed with global Ising entangling gates and arbitrary addressable single-qubit gates. We show that under certain circumstances the use of global operations can substantially improve the entangling gate count.

%B New Journal of Physics %8 2017/12/21 %G eng %U http://iopscience.iop.org/article/10.1088/1367-2630/aaa398 %R 10.1088/1367-2630/aaa398 %0 Journal Article %J Physical Review B %D 2017 %T Valley Blockade in a Silicon Double Quantum Dot %A Justin K. Perron %A Michael Gullans %A Jacob M. Taylor %A M. D. Stewart, Jr. %A Neil M. Zimmerman %XElectrical transport in double quantum dots (DQDs) illuminates many interesting features of the dots' carrier states. Recent advances in silicon quantum information technologies have renewed interest in the valley states of electrons confined in silicon. Here we show measurements of DC transport through a mesa-etched silicon double quantum dot. Comparing bias triangles (i.e., regions of allowed current in DQDs) at positive and negative bias voltages we find a systematic asymmetry in the size of the bias triangles at the two bias polarities. Asymmetries of this nature are associated with blocking of tunneling events due to the occupation of a metastable state. Several features of our data lead us to conclude that the states involved are not simple spin states. Rather, we develop a model based on selective filling of valley states in the DQD that is consistent with all of the qualitative features of our data.

%B Physical Review B %V 96 %P 205302 %8 2017/11/13 %G eng %U https://arxiv.org/abs/1607.06107 %N 20 %R 10.1103/PhysRevB.96.205302 %0 Journal Article %D 2017 %T Why Bohr was (Mostly) Right %A Jeffrey Bub %XAfter a discussion of the Frauchiger-Renner argument that no “singleworld” interpretation of quantum mechanics can be self-consistent, I propose a “Bohrian” alternative to many-worlds or QBism as the rational option.

%8 2017/11/05 %G eng %U https://arxiv.org/abs/1711.01604 %0 Journal Article %J Physical Review A %D 2016 %T Adiabatic optimization versus diffusion Monte Carlo %A Michael Jarret %A Stephen P. Jordan %A Brad Lackey %XMost experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here, we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-k-SAT at k=2,3,4.

%B Physical Review A %V 94 %P 042318 %8 2016/07/12 %G eng %U https://arxiv.org/abs/1607.03389 %0 Journal Article %J Physical Review A %D 2016 %T On the advantages of using relative phase Toffolis with an application to multiple control Toffoli optimization %A Dmitri Maslov %X Various implementations of the Toffoli gate up to a relative phase have been known for years. The advantage over regular Toffoli gate is their smaller circuit size. However, their use has been often limited to a demonstration of quantum control in designs such as those where the Toffoli gate is being applied last or otherwise for some specific reasons the relative phase does not matter. It was commonly believed that the relative phase deviations would prevent the relative phase Toffolis from being very helpful in practical large-scale designs. In this paper, we report three circuit identities that provide the means for replacing certain configurations of the multiple control Toffoli gates with their simpler relative phase implementations, up to a selectable unitary on certain qubits, and without changing the overall functionality. We illustrate the advantage via applying those identities to the optimization of the known circuits implementing multiple control Toffoli gates, and report the reductions in the CNOT-count, T-count, as well as the number of ancillae used. We suggest that a further study of the relative phase Toffoli implementations and their use may yield other optimizations. %B Physical Review A %V 93 %P 022311 %8 2016/02/10 %G eng %U http://arxiv.org/abs/1508.03273 %N 2 %R 10.1103/PhysRevA.93.022311 %0 Journal Article %J Physical Review Letters %D 2016 %T Anomalous broadening in driven dissipative Rydberg systems %A E. A. Goldschmidt %A T. Boulier %A R. C. Brown %A S. B. Koller %A J. T. Young %A Alexey V. Gorshkov %A S. L. Rolston %A J. V. Porto %X We observe interaction-induced broadening of the two-photon 5s-18s transition in 87Rb atoms trapped in a 3D optical lattice. The measured linewidth increases by nearly two orders of magnitude with increasing atomic density and excitation strength, with corresponding suppression of resonant scattering and enhancement of off-resonant scattering. We attribute the increased linewidth to resonant dipole-dipole interactions of 18s atoms with spontaneously created populations of nearby np states. Over a range of initial atomic densities and excitation strengths, the transition width is described by a single function of the steady-state density of Rydberg atoms, and the observed resonant excitation rate corresponds to that of a two-level system with the measured, rather than natural, linewidth. The broadening mechanism observed here is likely to have negative implications for many proposals with coherently interacting Rydberg atoms. %B Physical Review Letters %V 116 %P 113001 %8 2016/03/16 %G eng %U http://arxiv.org/abs/1510.08710 %N 11 %R 10.1103/PhysRevLett.116.113001 %0 Book %D 2016 %T Bananaworld: Quantum Mechanics for Primates %A Jeffrey Bub %XThis is intended to be a serious paper, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, since a theory of information is essentially a theory of probabilistic correlations. To make this clear, it suffices to consider measurements of two binary-valued observables, x with outcomes a = 0 or 1, performed by Alice in a region A, and y with outcomes b = 0 or 1 performed by Bob in a separated region B --or, to emphasize the banality of the phenomena, two ways of peeling a banana, resulting in one of two tastes. The imagined bananas of Bananaworld are non-standard, with operational or phenomenal probabilistic correlations for peelings and tastes that lie outside the polytope of local correlations. The 'no go' theorems tell us that we can't shoe-horn these correlations into a classical correlation polytope, which has the structure of a simplex, by supposing that something has been left out of the story, without giving up fundamental principles that define what we mean by a physical system. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are shown to be generic features of correlations that lie outside the local correlation polytope. As far as the conceptual problems are concerned, we might as well talk about bananas.

%I Oxford University Press %8 2012/11/13 %G eng %U http://arxiv.org/abs/1211.3062v2 %) Revised paperback edition, April 2018 %0 Journal Article %J XRDS %D 2016 %T Black Holes, Quantum Mechanics, and the Limits of Polynomial-time Computability %A Stephen P. Jordan %XWhich computational problems can be solved in polynomial-time and which cannot? Though seemingly technical, this question has wide-ranging implications and brings us to the heart of both theoretical computer science and modern physics.

%B XRDS %V 23 %P 30–33 %8 2016/09/20 %G eng %U http://doi.acm.org/10.1145/2983539 %R 10.1145/2983539 %0 Journal Article %J Physical Review B %D 2016 %T Causality and quantum criticality in long-range lattice models %A Mohammad F. Maghrebi %A Zhe-Xuan Gong %A Michael Foss-Feig %A Alexey V. Gorshkov %B Physical Review B %V 93 %P 125128 %8 2016/03/17 %G eng %U http://link.aps.org/doi/10.1103/PhysRevB.93.125128 %R 10.1103/PhysRevB.93.125128 %0 Journal Article %J Physical Review B %D 2016 %T Causality and quantum criticality with long-range interactions %A Mohammad F. Maghrebi %A Zhe-Xuan Gong %A Michael Foss-Feig %A Alexey V. Gorshkov %X Quantum lattice systems with long-range interactions often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model and a fermionic model with long-range interactions, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of long-range interactions, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent. %B Physical Review B %V 92 %P 125128 %8 2016/03/17 %G eng %U http://arxiv.org/abs/1508.00906 %N 12 %R 10.1103/PhysRevB.93.125128 %0 Journal Article %D 2016 %T Co-Designing a Scalable Quantum Computer with Trapped Atomic Ions %A Kenneth R. Brown %A Jaewan Kim %A Christopher Monroe %X The first generation of quantum computers are on the horizon, fabricated from quantum hardware platforms that may soon be able to tackle certain tasks that cannot be performed or modelled with conventional computers. These quantum devices will not likely be universal or fully programmable, but special-purpose processors whose hardware will be tightly co-designed with particular target applications. Trapped atomic ions are a leading platform for first generation quantum computers, but are also fundamentally scalable to more powerful general purpose devices in future generations. This is because trapped ion qubits are atomic clock standards that can be made identical to a part in 10^15, and their quantum circuit connectivity can be reconfigured through the use of external fields, without modifying the arrangement or architecture of the qubits themselves. In this article we show how a modular quantum computer of any size can be engineered from ion crystals, and how the wiring between ion trap qubits can be tailored to a variety of applications and quantum computing protocols. %8 2016/02/09 %G eng %U http://arxiv.org/abs/1602.02840 %0 Journal Article %J Physical Review A %D 2016 %T Collective phases of strongly interacting cavity photons %A Ryan M. Wilson %A Khan W. Mahmud %A Anzi Hu %A Alexey V. Gorshkov %A Mohammad Hafezi %A Michael Foss-Feig %XWe study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-12 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.

%B Physical Review A %V 94 %P 033801 %8 2016/09/01 %G eng %U http://arxiv.org/abs/1601.06857 %N 3 %R http://dx.doi.org/10.1103/PhysRevA.94.033801 %0 Journal Article %D 2016 %T A Complete Characterization of Unitary Quantum Space %A Bill Fefferman %A Cedric Yen-Yu Lin %X We give two complete characterizations of unitary quantum space-bounded classes. The first is based on the Matrix Inversion problem for well-conditioned matrices. We show that given the size-n efficient encoding of a 2O(k(n))×2O(k(n)) well-conditioned matrix H, approximating a particular entry of H−1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation. In particular, the problem of computing entries of H−1 for an explicit well-conditioned n×n matrix H is complete for unitary quantum logspace. We then show that the problem of approximating to high precision the least eigenvalue of a positive semidefinite matrix H, encoded as a circuit, gives a second characterization of unitary quantum space complexity. In the process we also establish an equivalence between unitary quantum space-bounded classes and certain QMA proof systems. As consequences, we establish that QMA with exponentially small completeness-soundness gap is equal to PSPACE, that determining whether a local Hamiltonian is frustration-free is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states gives less computational power than the ability to prepare the ground state of a generic local Hamiltonian. %8 2016/04/05 %G eng %U http://arxiv.org/abs/1604.01384 %0 Journal Article %J Quantum Information and Computation %D 2016 %T Complexity of the XY antiferromagnet at fixed magnetization %A Andrew M. Childs %A David Gosset %A Zak Webb %X We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this, we strengthen a previous result by establishing QMA-completeness for approximating the ground energy of the Bose-Hubbard model on simple graphs. Using a connection between the XY and Bose-Hubbard models that we exploited in previous work, this establishes QMA-completeness of the XY model. %B Quantum Information and Computation %V 16 %P 1-18 %8 2016/01/01 %G eng %U http://arxiv.org/abs/1503.07083v1 %N 1-2 %0 Conference Paper %B Computational Security of Quantum Encryption. In: Nascimento A., Barreto P. (eds) Information Theoretic Security. %D 2016 %T Computational Security of Quantum Encryption %A Gorjan Alagic %A Anne Broadbent %A Bill Fefferman %A Tommaso Gagliardoni %A Christian Schaffner %A Michael St. Jules %XQuantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of another relevant topic: the encryption of quantum data in the computational setting. In this direction, we establish quantum versions of several fundamental classical results. First, we develop natural definitions for private-key and public-key encryption schemes for quantum data. We then define notions of semantic security and indistinguishability, and, in analogy with the classical work of Goldwasser and Micali, show that these notions are equivalent. Finally, we construct secure quantum encryption schemes from basic primitives. In particular, we show that quantum-secure one-way functions imply IND-CCA1-secure symmetric-key quantum encryption, and that quantum-secure trapdoor one-way permutations imply semantically-secure public-key quantum encryption.

%B Computational Security of Quantum Encryption. In: Nascimento A., Barreto P. (eds) Information Theoretic Security. %8 2016/11/10 %G eng %U https://link.springer.com/chapter/10.1007%2F978-3-319-49175-2_3 %0 Journal Article %J Nature %D 2016 %T Demonstration of a small programmable quantum computer with atomic qubits %A S. Debnath %A N. M. Linke %A C. Figgatt %A K. A. Landsman %A K. Wright %A C. Monroe %XQuantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here, we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully-connected set of gate operations that are native to the hardware and have a mean fidelity of 98 %. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa (DJ) and Bernstein-Vazirani (BV) algorithms with average success rates of 95 % and 90 %, respectively. We also perform a coherent quantum Fourier transform (QFT) on five trappedion qubits for phase estimation and period finding with average fidelities of 62 % and 84 %, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

%B Nature %V 536 %P 63-66 %8 2016/08/04 %G eng %U http://www.nature.com/nature/journal/v536/n7614/full/nature18648.html %N 7614 %R 10.1038/nature18648 %0 Journal Article %J Physical Review A %D 2016 %T Detecting Consistency of Overlapping Quantum Marginals by Separability %A Jianxin Chen %A Zhengfeng Ji %A Nengkun Yu %A Bei Zeng %X The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general, and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known $k$-symmetric extension criterion for separability. %B Physical Review A %V 93 %P 032105 %8 2016/03/03 %G eng %U http://arxiv.org/abs/1509.06591 %N 3 %R 10.1103/PhysRevA.93.032105 %0 Journal Article %J Physical Review X %D 2016 %T Double Quantum Dot Floquet Gain Medium %A J. Stehlik %A Y.-Y. Liu %A C. Eichler %A T. R. Hartke %A X. Mi %A Michael Gullans %A J. M. Taylor %A J. R. Petta %XStrongly driving a two-level quantum system with light leads to a ladder of Floquet states separated by the photon energy. Nanoscale quantum devices allow the interplay of confined electrons, phonons, and photons to be studied under strong driving conditions. Here we show that a single electron in a periodically driven DQD functions as a "Floquet gain medium," where population imbalances in the DQD Floquet quasi-energy levels lead to an intricate pattern of gain and loss features in the cavity response. We further measure a large intra-cavity photon number n_c in the absence of a cavity drive field, due to equilibration in the Floquet picture. Our device operates in the absence of a dc current -- one and the same electron is repeatedly driven to the excited state to generate population inversion. These results pave the way to future studies of non-classical light and thermalization of driven quantum systems.

%B Physical Review X %V 6 %P 041027 %8 2016/11/07 %G eng %U http://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.041027 %R 10.1103/PhysRevX.6.041027 %0 Journal Article %J Physical Review Letters %D 2016 %T Effective Field Theory for Rydberg Polaritons %A Michael Gullans %A J. D. Thompson %A Y. Wang %A Q. -Y. Liang %A V. Vuletic %A M. D. Lukin %A Alexey V. Gorshkov %XWe study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT). We develop an EFT in one dimension and show how a suitably long medium can be used to prepare shallow N-body bound states. We then derive the effective N-body interaction potential for Rydberg polaritons and the associated N-body contact force that arises in the EFT. We use the contact force to find the leading order corrections to the binding energy of the N-body bound states and determine the photon number at which the EFT description breaks down. We find good agreement throughout between the predictions of EFT and numerical simulations of the exact two and three photon wavefunction transmission.

%B Physical Review Letters %V 117 %P 113601 %8 2016/09/09 %G eng %U http://arxiv.org/abs/1605.05651 %N 11 %R http://dx.doi.org/10.1103/PhysRevLett.117.113601 %0 Journal Article %D 2016 %T Entanglement and spin-squeezing without infinite-range interactions %A Michael Foss-Feig %A Zhe-Xuan Gong %A Alexey V. Gorshkov %A Charles W. Clark %XInfinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law (1/r α ) interactions in D dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small α the scaling of squeezing with system size is identical to the infinite-range (α = 0) case. This indifference to the interaction range persists up to a critical value α = 2D/3, above which squeezing degrades continuously. Boundaryinduced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.

%8 2016/12/22 %G eng %U https://arxiv.org/abs/1612.07805 %0 Journal Article %J Physical Review B %D 2016 %T Entangling distant resonant exchange qubits via circuit quantum electrodynamics %A V. Srinivasa %A J.M. Taylor %A C. Tahan %XWe investigate a hybrid quantum system consisting of spatially separated resonant exchange qubits, defined in three-electron semiconductor triple quantum dots, that are coupled via a superconducting transmission line resonator. Drawing on methods from circuit quantum electrodynamics and Hartmann-Hahn double resonance techniques, we analyze three specific approaches for implementing resonator-mediated two-qubit entangling gates in both dispersive and resonant regimes of interaction. We calculate entangling gate fidelities as well as the rate of relaxation via phonons for resonant exchange qubits in silicon triple dots and show that such an implementation is particularly well-suited to achieving the strong coupling regime. Our approach combines the favorable coherence properties of encoded spin qubits in silicon with the rapid and robust long-range entanglement provided by circuit QED systems.

%B Physical Review B %V 94 %P 205421 %8 2016/11/16 %G eng %U https://doi.org/10.1103/PhysRevB.94.205421 %N 20 %R 10.1103/PhysRevB.94.205421 %0 Journal Article %D 2016 %T Experimental demonstration of quantum fault tolerance %A N. M. Linke %A M. Gutierrez %A K. A. Landsman %A C. Figgatt %A S. Debnath %A K. R. Brown %A C. Monroe %XQuantum computers will eventually reach a size at which quantum error correction (QEC) becomes imperative. In order to make quantum information robust to errors introduced by qubit imperfections and flawed control operations, QEC protocols encode a logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent correction or detection of errors without destroying the logical state itself through direct measurement. While several experiments have shown a reduction of high intrinsic or artificially introduced errors in logical qubits, fault-tolerant encoding of a logical qubit has never been demonstrated. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. This advantage persists in the face of large added error rates and experimental calibration errors.

%8 2016/11/21 %G eng %U https://arxiv.org/abs/1611.06946 %0 Conference Paper %B 20th Annual Conference on Quantum Information Processing (QIP) %D 2016 %T Exponential Separation of Quantum Communication and Classical Information %A Anurag Anshu %A Dave Touchette %A Penghui Yao %A Nengkun Yu %XWe exhibit a Boolean function for which the quantum communication complexity is exponentially larger than the classical information complexity. An exponential separation in the other direction was already known from the work of Kerenidis et. al. [SICOMP 44, pp. 1550-1572], hence our work implies that these two complexity measures are incomparable. As classical information complexity is an upper bound on quantum information complexity, which in turn is equal to amortized quantum communication complexity, our work implies that a tight direct sum result for distributional quantum communication complexity cannot hold. The function we use to present such a separation is the Symmetric k-ary Pointer Jumping function introduced by Rao and Sinha [ECCC TR15-057], whose classical communication complexity is exponentially larger than its classical information complexity. In this paper, we show that the quantum communication complexity of this function is polynomially equivalent to its classical communication complexity. The high-level idea behind our proof is arguably the simplest so far for such an exponential separation between information and communication, driven by a sequence of round-elimination arguments, allowing us to simplify further the approach of Rao and Sinha.

As another application of the techniques that we develop, we give a simple proof for an optimal trade-off between Alice's and Bob's communication while computing the related Greater-Than function on n bits: say Bob communicates at most b bits, then Alice must send n/exp(O(b)) bits to Bob. This holds even when allowing pre-shared entanglement. We also present a classical protocol achieving this bound.

Recent technical advances have sparked renewed interest in physical systems that couple simultaneously to different parts of the electromagnetic spectrum, thus enabling transduction of signals between vastly different frequencies at the level of single photons. Such hybrid systems have demonstrated frequency conversion of classical signals and have the potential of enabling quantum state transfer, e.g., between superconducting circuits and traveling optical signals. This Letter describes a simple approach for the theoretical characterization of performance for quantum transducers. Given that, in practice, one cannot attain ideal one-to-one quantum conversion, we will explore how well the transducer performs in various scenarios ranging from classical signal detection to applications for quantum information processing. While the performance of the transducer depends on the particular application in which it enters, we show that the performance can be characterized by defining two simple parameters: the signal transfer efficiency

We give a finite presentation by generators and relations of unitary operators expressible over the {CNOT, T, X} gate set, also known as CNOT-dihedral operators. To this end, we introduce a notion of normal form for CNOT-dihedral circuits and prove that every CNOT-dihedral operator admits a unique normal form. Moreover, we show that in the presence of certain structural rules only finitely many circuit identities are required to reduce an arbitrary CNOT-dihedral circuit to its normal form. By appropriately restricting our relations, we obtain a finite presentation of unitary operators expressible over the {CNOT, T } gate set as a corollary.

%8 2016/12/31 %G eng %U https://arxiv.org/abs/1701.00140 %0 Journal Article %J Physical Review B %D 2016 %T Flight of a heavy particle nonlinearly coupled to a quantum bath %A Mohammad F. Maghrebi %A Matthias Krüger %A Mehran Kardar %X Fluctuation and dissipation are by-products of coupling to the `environment.' The Caldeira-Leggett model, a successful paradigm of quantum Brownian motion, views the environment as a collection of harmonic oscillators linearly coupled to the system. However, symmetry considerations may forbid a linear coupling, e.g. for a neutral particle in quantum electrodynamics. We argue that nonlinear couplings can lead to a fundamentally different behavior. Specifically, we consider a heavy particle quadratically coupled to quantum fluctuations of the bath. In one dimension the particle undergoes anomalous diffusion, unfolding as a power-law distribution in space, reminiscent of L\'{e}vy flights. We suggest condensed matter analogs where similar effects may arise. %B Physical Review B %V 93 %P 014309 %8 2016/01/28 %G eng %U http://arxiv.org/abs/1508.00582 %N 1 %R 10.1103/PhysRevB.93.014309 %0 Journal Article %J Physical Review Letters %D 2016 %T Grover search and the no-signaling principle %A Ning Bao %A Adam Bouland %A Stephen P. Jordan %XFrom an information processing point of view, two of the key properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply superluminal signaling, and despite a form of exponential parallelism, quantum mechanics does not imply polynomial-time brute force solution of NP-complete problems. Here, we investigate the degree to which these two properties are connected. We examine four classes of deviations from quantum mechanics, for which we draw inspiration from the literature on the black hole information paradox: nonunitary dynamics, non-Born-rule measurement, cloning, and postselection. We find that each model admits superluminal signaling if and only if it admits a query complexity speedup over Grover's algorithm. Furthermore, we show that the physical resources required to send a superluminal signal scale polynomially with the resources needed to speed up Grover's algorithm. Hence, one can perform a physically reasonable experiment demonstrating superluminal signaling if and only if one can perform a reasonable experiment inducing a speedup over Grover's algorithm.

%B Physical Review Letters %V 117 %P 120501 %8 2016/09/14 %G eng %U http://arxiv.org/abs/1511.00657 %0 Journal Article %J Nature Photonics %D 2016 %T High resolution adaptive imaging of a single atom %A J. D. Wong-Campos %A K. G. Johnson %A Brian Neyenhuis %A J. Mizrahi %A Chris Monroe %XWe report the optical imaging of a single atom with nanometer resolution using an adaptive optical alignment technique that is applicable to general optical microscopy. By decomposing the image of a single laser-cooled atom, we identify and correct optical aberrations in the system and realize an atomic position sensitivity of ≈ 0.5 nm/Hz−−−√ with a minimum uncertainty of 1.7 nm, allowing the direct imaging of atomic motion. This is the highest position sensitivity ever measured for an isolated atom, and opens up the possibility of performing out-of-focus 3D particle tracking, imaging of atoms in 3D optical lattices or sensing forces at the yoctonewton (10−24 N) scale.

%B Nature Photonics %P 606-610 %8 2016/07/18 %G eng %U https://www.nature.com/nphoton/journal/v10/n9/full/nphoton.2016.136.html %N 10 %R 10.1038/nphoton.2016.136 %0 Journal Article %J Physical Review A %D 2016 %T A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions %A Saurabh Paul %A P. R. Johnson %A Eite Tiesinga %XWe show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pair-wise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two- and three-body interactions for scattering from van-der-Waals potentials and near Fano-Feshbach resonances. For van-der-Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pair-wise interaction can only be turned off for species with a small negative scattering length, leaving the 88Sr isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.

%B Physical Review A %V 93 %P 043616 %8 2016/04/19 %G eng %U http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.043616 %N 4 %R 10.1103/PhysRevA.93.043616 %0 Journal Article %J Physical Review Letters %D 2016 %T Interacting atomic interferometry for rotation sensing approaching the Heisenberg Limit %A Stephen Ragole %A Jacob M. Taylor %XAtom interferometers provide exquisite measurements of the properties of non-inertial frames. While atomic interactions are typically detrimental to good sensing, efforts to harness entanglement to improve sensitivity remain tantalizing. Here we explore the role of interactions in an analogy between atomic gyroscopes and SQUIDs, motivated by recent experiments realizing ring shaped traps for ultracold atoms. We explore the one-dimensional limit of these ring systems with a moving weak barrier, such as that provided by a blue-detuned laser beam. In this limit, we employ Luttinger liquid theory and find an analogy with the superconducting phase-slip qubit, in which the topological charge associated with persistent currents can be put into superposition. In particular, we find that strongly-interacting atoms in such a system could be used for precision rotation sensing. We compare the performance of this new sensor to an equivalent non-interacting atom interferometer, and find improvements in sensitivity and bandwidth beyond the atomic shot-noise limit.

%B Physical Review Letters %V 117 %P 203002 %8 2016/11/11 %G eng %U https://doi.org/10.1103/PhysRevLett.117.203002 %N 20 %R 10.1103/PhysRevLett.117.203002 %0 Journal Article %D 2016 %T Joint product numerical range and geometry of reduced density matrices %A Jianxin Chen %A Cheng Guo %A Zhengfeng Ji %A Yiu-Tung Poon %A Nengkun Yu %A Bei Zeng %A Jie Zhou %X The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection Θ is convex in R3. The boundary ∂Θ of Θ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti's theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range Π of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that ruled surface emerge naturally when taking a convex hull of Π. We show that, a ruled surface on ∂Θ sitting in Π has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of Θ, with two boundary pieces of symmetry breaking origin separated by two gapless lines. %8 2016/06/23 %G eng %U http://arxiv.org/abs/1606.07422 %0 Journal Article %J Physical Review B %D 2016 %T Kaleidoscope of quantum phases in a long-range interacting spin-1 chain %A Zhe-Xuan Gong %A Mohammad F. Maghrebi %A Anzi Hu %A Michael Foss-Feig %A Philip Richerme %A Christopher Monroe %A Alexey V. Gorshkov %X Motivated by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as 1/rα, using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (non-frustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for α≲3, long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a U(1) continuous symmetry, and introduce an exotic tricritical point with no direct parallel in short-range interacting spin chains. We show that the main signatures of all five phases found could be observed experimentally in the near future. %B Physical Review B %V 93 %P 205115 %8 2016/05/11 %G eng %U http://arxiv.org/abs/1510.02108 %N 20 %R http://dx.doi.org/10.1103/PhysRevB.93.205115 %0 Journal Article %J Physical Review B %D 2016 %T Landauer formulation of photon transport in driven systems %A Chiao-Hsuan Wang %A Jacob M. Taylor %XUnderstanding the behavior of light in non-equilibrium scenarios underpins much of quantum optics and optical physics. While lasers provide a severe example of a non-equilibrium problem, recent interests in the near-equilibrium physics of photon `gases', such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one reexamine some near-equilibrium cases. Here we consider how a sinusoidal parametric coupling between two semi-infinite photonic transmission lines leads to the creation and flow of photons between the two lines. Our approach provides a photonic analogue to the Landauer transport formula, and using non-equilbrium Green's functions, we can extend it to the case of an interacting region between two photonic `leads' where the sinusoid frequency plays the role of a voltage bias. Crucially, we identify both the mathematical framework and the physical regime in which photonic transport is directly analogous to electronic transport, and regimes in which other new behavior such as two-mode squeezing can emerge.

%B Physical Review B %V 94 %P 155437 %8 2016/10/20 %G eng %U https://doi.org/10.1103/PhysRevB.94.155437 %N 15 %R 10.1103/PhysRevB.94.155437 %0 Journal Article %J Journal of Statistical Mechanics: Theory and Experiment %D 2016 %T Lattice Laughlin states on the torus from conformal field theory %A Abhinav Deshpande %A Anne E B Nielsen %X Conformal field theory has turned out to be a powerful tool to derive two-dimensional lattice models displaying fractional quantum Hall physics. So far most of the work has been for lattices with open boundary conditions in at least one of the two directions, but it is desirable to also be able to handle the case of periodic boundary conditions. Here, we take steps in this direction by deriving analytical expressions for a family of conformal field theory states on the torus that is closely related to the family of bosonic and fermionic Laughlin states. We compute how the states transform when a particle is moved around the torus and when the states are translated or rotated, and we provide numerical evidence in particular cases that the states become orthonormal up to a common factor for large lattices. We use these results to find the S -matrix of the states, which turns out to be the same as for the continuum Laughlin states. Finally, we show that when the states are defined on a square lattice with suitable lattice spacing they practically coincide with the Laughlin states restricted to a lattice. %B Journal of Statistical Mechanics: Theory and Experiment %V 2016 %P 013102 %8 2016/01/28 %G eng %U http://stacks.iop.org/1742-5468/2016/i=1/a=013102 %0 Journal Article %J New Journal of Physics %D 2016 %T Many-body decoherence dynamics and optimised operation of a single-photon switch %A Callum R. Murray %A Alexey V. Gorshkov %A Thomas Pohl %XWe develop a theoretical framework to characterize the decoherence dynamics due to multi-photon scattering in an all-optical switch based on Rydberg atom induced nonlinearities. By incorporating the knowledge of this decoherence process into optimal photon storage and retrieval strategies, we establish optimised switching protocols for experimentally relevant conditions, and evaluate the corresponding limits in the achievable fidelities. Based on these results we work out a simplified description that reproduces recent experiments [arXiv:1511.09445] and provides a new interpretation in terms of many-body decoherence involving multiple incident photons and multiple gate excitations forming the switch. Aside from offering insights into the operational capacity of realistic photon switching capabilities, our work provides a complete description of spin wave decoherence in a Rydberg quantum optics setting, and has immediate relevance to a number of further applications employing photon storage in Rydberg media.

%B New Journal of Physics %V 18 %P 092001 %8 2016/09/13 %G eng %U http://iopscience.iop.org/article/10.1088/1367-2630/18/9/092001 %R 10.1088/1367-2630/18/9/092001 %0 Journal Article %J Nature Physics %D 2016 %T Many-body localization in a quantum simulator with programmable random disorder %A Jacob Smith %A Aaron Lee %A Philip Richerme %A Brian Neyenhuis %A Paul W. Hess %A Philipp Hauke %A Markus Heyl %A David A. Huse %A Christopher Monroe %XWhen a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even within a closed (or reversible) quantum system, where unitary time evolution retains all information about its initial state, subsystems can still thermalize using the rest of the system as an effective heat bath. Exceptions to quantum thermalization have been predicted and observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize in spite of strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. Here we experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium. We observe the essential signatures of MBL: memory retention of the initial state, a Poissonian distribution of energy level spacings, and entanglement growth in the system at long times. Our platform can be scaled to higher numbers of spins, where detailed modeling of MBL becomes impossible due to the complexity of representing such entangled quantum states. Moreover, the high degree of control in our experiment may guide the use of MBL states as potential quantum memories in naturally disordered quantum systems.

%B Nature Physics %8 2016/06/06 %G eng %U http://arxiv.org/abs/1508.07026v1 %R 10.1038/nphys3783 %0 Journal Article %D 2016 %T Mapping constrained optimization problems to quantum annealing with application to fault diagnosis %A Bian, Zhengbing %A Chudak, Fabian %A Israel, Robert %A Lackey, Brad %A Macready, William G %A Roy, Aidan %X Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally-structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. In contrast, global embedding techniques generate a hardware independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of D-Wave's QA hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D-Wave's hardware to circuit-based fault-diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Further, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware. %G eng %U http://arxiv.org/abs/1603.03111 %0 Journal Article %J Frontiers in ICT %D 2016 %T Mapping contrained optimization problems to quantum annealing with application to fault diagnosis %A Bian, Zhengbing %A Chudak, Fabian %A Robert Brian Israel %A Brad Lackey %A Macready, William G %A Aiden Roy %XCurrent quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping Boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular, we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. By contrast, global embedding techniques generate a hardware-independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of the D-Wave hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D- Wave’s QA hardware to circuit-based fault diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000 N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Furthermore, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware.

%B Frontiers in ICT %V 3 %P 14 %8 2016/07/28 %G eng %U http://journal.frontiersin.org/article/10.3389/fict.2016.00014/full %0 Journal Article %J Nature Communications %D 2016 %T Multiple scattering dynamics of fermions at an isolated p-wave resonance %A Ryan Thomas %A Kris O. Roberts %A Eite Tiesinga %A Andrew C.J. Wade %A P. Blair Blakie %A Amita B. Deb %A Niels Kjærgaard %XThe wavefunction for indistinguishable fermions is anti-symmetric under particle exchange, which directly leads to the Pauli exclusion principle, and hence underlies the structure of atoms and the properties of almost all materials. In the dynamics of collisions between two indistinguishable fermions this requirement strictly prohibits scattering into 90 degree angles. Here we experimentally investigate the collisions of ultracold clouds fermionic

Statistical mechanics can predict thermal equilibrium states for most classical systems, but for an isolated quantum system there is no general understanding on how equilibrium states dynamically emerge from the microscopic Hamiltonian. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale and, instead, relax to quasi-stationary prethermal states that can be described by statistical mechanics when approximately conserved quantities are appropriately included in a generalized Gibbs ensemble (GGE). Here we experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse field Ising Hamiltonian following a sudden quench. For sufficiently long-ranged interactions the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. In this case, the prethermal state cannot be described by a GGE, but rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a significantly broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.

%8 2016/08/02 %G eng %U https://arxiv.org/abs/1608.00681 %0 Journal Article %D 2016 %T Observation of Optomechanical Quantum Correlations at Room Temperature %A T. P. Purdy %A K. E. Grutter %A K. Srinivasan %A J. M. Taylor %XBy shining laser light through a nanomechanical beam, we measure the beam's thermally driven vibrations and perturb its motion with optical forces at a level dictated by the Heisenberg measurement-disturbance uncertainty relation. Such quantum backaction is typically difficult to observe at room temperature where the motion driven by optical quantum intensity fluctuations is many orders of magnitude smaller than the thermal motion. We demonstrate a cross-correlation technique to distinguish optically driven motion from thermally driven motion, observing this quantum backaction signature up to room temperature. While it is often difficult to absolutely calibrate optical detection, we use the scale of the quantum correlations, which is determined by fundamental constants, to gauge the size of thermal motion, demonstrating a path towards absolute thermometry with quantum mechanically calibrated ticks.

%8 2016/05/18 %G eng %U http://arxiv.org/abs/1605.05664 %0 Journal Article %J Quantum Information and Computation %D 2016 %T Optimal ancilla-free Clifford+T approximation of z-rotations %A Neil J. Ross %A Peter Selinger %XWe consider the problem of decomposing arbitrary single-qubit z-rotations into ancilla-free Clifford+T circuits, up to given epsilon. We present a new efficient algorithm for solving this problem optimally, i.e., for finding the shortest possible circuit whatsoever for the given problem instance. The algorithm requires a factoring oracle (such as a quantum computer). Even in the absence of a factoring oracle, the algorithm is still near-optimal: In this case, it finds a solution of T-count m + O(log(log(1/epsilon))), where m is the T-count of the second-to-optimal solution. In the typical case, this yields circuit decompositions of T-count 3log_2(1/epsilon) + O(log(log(1/epsilon))).

%B Quantum Information and Computation %V 16 %P 901-953 %G eng %U http://arxiv.org/abs/1403.2975v2 %N 11-12 %0 Journal Article %J Quantum Information & Computation %D 2016 %T Optimal and asymptotically optimal NCT reversible circuits by the gate types %A Dmitri Maslov %XWe report optimal and asymptotically optimal reversible circuits composed of NOT, CNOT, and Toffoli (NCT) gates, keeping the count by the subsets of the gate types used. This study fine tunes the circuit complexity figures for the realization of reversible functions via reversible NCT circuits. An important consequence is a result on the limitation of the use of the T-count quantum circuit metric popular in applications.

%B Quantum Information & Computation %V 16 %P 1096-1112 %8 2016/08/23 %G eng %U http://arxiv.org/abs/1602.02627 %N 13 & 14 %0 Journal Article %J 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) %D 2016 %T Optimal quantum algorithm for polynomial interpolation %A Andrew M. Childs %A Wim van Dam %A Shih-Han Hung %A Igor E. Shparlinski %XWe consider the number of quantum queries required to determine the coefficients of a degree-d polynomial over GF(q). A lower bound shown independently by Kane and Kutin and by Meyer and Pommersheim shows that d/2+1/2 quantum queries are needed to solve this problem with bounded error, whereas an algorithm of Boneh and Zhandry shows that d quantum queries are sufficient. We show that the lower bound is achievable: d/2+1/2 quantum queries suffice to determine the polynomial with bounded error. Furthermore, we show that d/2+1 queries suffice to achieve probability approaching 1 for large q. These upper bounds improve results of Boneh and Zhandry on the insecurity of cryptographic protocols against quantum attacks. We also show that our algorithm's success probability as a function of the number of queries is precisely optimal. Furthermore, the algorithm can be implemented with gate complexity poly(log q) with negligible decrease in the success probability.

%B 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) %V 55 %P 16:1--16:13 %8 2016/03/01 %@ 978-3-95977-013-2 %G eng %U http://arxiv.org/abs/1509.09271 %R http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.16 %0 Journal Article %J Physical Review A %D 2016 %T Optimal state discrimination and unstructured search in nonlinear quantum mechanics %A Andrew M. Childs %A Joshua Young %X Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics. %B Physical Review A %V 93 %P 022314 %8 2016/02/11 %G eng %U http://arxiv.org/abs/1507.06334 %N 2 %R 10.1103/PhysRevA.93.022314 %0 Journal Article %J Physical Review A %D 2016 %T Optimized tomography of continuous variable systems using excitation counting %A Shen, Chao %A Heeres, Reinier W. %A Reinhold, Philip %A Jiang, Luyao %A Yi-Kai Liu %A Schoelkopf, Robert J. %A Jiang, Liang %XWe propose a systematic procedure to optimize quantum state tomography protocols for continuous variable systems based on excitation counting preceded by a displacement operation. Compared with conventional tomography based on Husimi or Wigner function measurement, the excitation counting approach can significantly reduce the number of measurement settings. We investigate both informational completeness and robustness, and provide a bound of reconstruction error involving the condition number of the sensing map. We also identify the measurement settings that optimize this error bound, and demonstrate that the improved reconstruction robustness can lead to an order-of-magnitude reduction of estimation error with given resources. This optimization procedure is general and can incorporate prior information of the unknown state to further simplify the protocol.

%B Physical Review A %V 94 %P 052327 %8 2016/11/21 %G eng %U http://link.aps.org/doi/10.1103/PhysRevA.94.052327 %R 10.1103/PhysRevA.94.052327 %0 Journal Article %D 2016 %T Performance of QAOA on Typical Instances of Constraint Satisfaction Problems with Bounded Degree %A Cedric Yen-Yu Lin %A Yechao Zhu %X We consider constraint satisfaction problems of bounded degree, with a good notion of "typicality", e.g. the negation of the variables in each constraint is taken independently at random. Using the quantum approximate optimization algorithm (QAOA), we show that μ+Ω(1/D−−√) fraction of the constraints can be satisfied for typical instances, with the assignment efficiently produced by QAOA. We do so by showing that the averaged fraction of constraints being satisfied is μ+Ω(1/D−−√), with small variance. Here μ is the fraction that would be satisfied by a uniformly random assignment, and D is the number of constraints that each variable can appear. CSPs with typicality include Max-kXOR and Max-kSAT. We point out how it can be applied to determine the typical ground-state energy of some local Hamiltonians. We also give a similar result for instances with "no overlapping constraints", using the quantum algorithm. We sketch how the classical algorithm might achieve some partial result. %8 2016/01/08 %G eng %U http://arxiv.org/abs/1601.01744 %0 Journal Article %J Physical Review A %D 2016 %T Photoassociation of spin polarized Chromium %A Jahn Rührig %A Tobias Bäuerle %A Paul S. Julienne %A Eite Tiesinga %A Tilman Pfau %X We report the homonuclear photoassociation (PA) of ultracold 52Cr atoms in an optical dipole trap. This constitutes the first measurement of PA in an element with total electron spin S~>1. Although Cr, with its 7S3 ground and 7P4,3,2 excited states, is expected to have a complicated PA spectrum we show that a spin polarized cloud exhibits a remarkably simple PA spectrum when circularly polarized light is applied. Over a scan range of 20 GHz below the 7P3 asymptote we observe two distinct vibrational series each following a LeRoy-Bernstein law for a C3/R3 potential with excellent agreement. We determine the C3 coefficients of the Hund's case c) relativistic adiabatic potentials to be -1.83±0.02 a.u. and -1.46±0.01a.u.. Theoretical non-rotating Movre-Pichler calculations enable a first assignment of the series to Ω=6u and 5g potential energy curves. In a different set of experiments we disturb the selection rules by a transverse magnetic field which leads to additional PA series. %B Physical Review A %V 93 %P 021406 %8 2016/02/29 %G eng %U http://arxiv.org/abs/1512.04378 %N 2 %R 10.1103/PhysRevA.93.021406 %0 Journal Article %J IEEE Transactions on Computers %D 2016 %T Practical Approximation of Single-Qubit Unitaries by Single-Qubit Quantum Clifford and T Circuits %A Vadym Kliuchnikov %A Dmitri Maslov %A Michele Mosca %XWe present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation down to size 10-15, resulting in the optimal single-qubit circuit designs required for implementation of scalable quantum algorithms. Our implementation along with the experimental results are available in the public domain.

%B IEEE Transactions on Computers %V 65 %P 161 - 172 %8 2016/01/01 %G eng %U http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7056491http://xplorestaging.ieee.org/ielx7/12/7350319/7056491.pdf?arnumber=7056491 %N 1 %! IEEE Trans. Comput. %R 10.1109/TC.2015.2409842 %0 Journal Article %J Physical Review A %D 2016 %T Pure-state tomography with the expectation value of Pauli operators %A Xian Ma %A Tyler Jackson %A Hui Zhou %A Jianxin Chen %A Dawei Lu %A Michael D. Mazurek %A Kent A.G. Fisher %A Xinhua Peng %A David Kribs %A Kevin J. Resch %A Zhengfeng Ji %A Bei Zeng %A Raymond Laflamme %XWe examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary n-qubit pure state among all quantum states. We show that only 11 Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with 16 measurements, and only 31 Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with 64 measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.

%B Physical Review A %V 93 %P 032140 %8 2016/03/31 %G eng %U http://arxiv.org/abs/1601.05379 %N 3 %R http://dx.doi.org/10.1103/PhysRevA.93.032140 %0 Journal Article %J Physical Review A %D 2016 %T Quantifying the coherence of pure quantum states %A Jianxin Chen %A Nathaniel Johnston %A Chi-Kwong Li %A Sarah Plosker %XIn recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an explicit characterization of the closest incoherent state to a given pure state under the trace distance measure of coherence, and we affirm a recent conjecture that the ℓ1 measure of coherence of a pure state is never smaller than its relative entropy of coherence. We then use our result to show that the states maximizing the trace distance of coherence are exactly the maximally coherent states, and we derive a new inequality relating the negativity and distillable entanglement of pure states.

%B Physical Review A %V 94 %P 042313 %8 2016/10/07 %G eng %U https://doi.org/10.1103/PhysRevA.94.042313 %N 4 %R 10.1103/PhysRevA.94.042313 %0 Journal Article %D 2016 %T Quantum Merlin Arthur with Exponentially Small Gap %A Bill Fefferman %A Cedric Yen-Yu Lin %X We study the complexity of QMA proof systems with inverse exponentially small promise gap. We show that this class can be exactly characterized by PSPACE, the class of problems solvable with a polynomial amount of memory. As applications we show that a "precise" version of the Local Hamiltonian problem is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states is not as powerful as the ability to prepare the ground state of general Local Hamiltonians. %8 2016/01/08 %G eng %U http://arxiv.org/abs/1601.01975 %0 Journal Article %J Physical Review B %D 2016 %T A Quantum Model for an Entropic Spring %A Chiao-Hsuan Wang %A J. M. Taylor %XMotivated by understanding the emergence of thermodynamic restoring forces and oscillations, we develop a quantum-mechanical model of a bath of spins coupled to the elasticity of a material. We show our model reproduces the behavior of a variety of entropic springs while enabling investigation of non-equilibrium resonator states in the quantum domain. We find our model emerges naturally in disordered elastic media such as glasses, and is an additional, expected effect in systems with anomalous specific heat and 1/f noise at low temperatures due to two-level systems that fluctuate.

%B Physical Review B %V 93 %P 214102 %8 2016/06/01 %G eng %U http://arxiv.org/abs/1507.08658v1 %N 21 %R http://dx.doi.org/10.1103/PhysRevB.93.214102 %0 Journal Article %D 2016 %T On Quantum Obfuscation %A Gorjan Alagic %A Bill Fefferman %X Encryption of data is fundamental to secure communication in the modern world. Beyond encryption of data lies obfuscation, i.e., encryption of functionality. It is well-known that the most powerful means of obfuscating classical programs, so-called ``black-box obfuscation',' is provably impossible [Barak et al '12]. However, several recent results have yielded candidate schemes that satisfy a definition weaker than black-box, and yet still have numerous applications. In this work, we initialize the rigorous study of obfuscating programs via quantum-mechanical means. We define notions of quantum obfuscation which encompass several natural variants. The input to the obfuscator can describe classical or quantum functionality, and the output can be a circuit description or a quantum state. The obfuscator can also satisfy one of a number of obfuscation conditions: black-box, information-theoretic black-box, indistinguishability, and best possible; the last two conditions come in three variants: perfect, statistical, and computational. We discuss many applications, including CPA-secure quantum encryption, quantum fully-homomorphic encryption, and public-key quantum money. We then prove several impossibility results, extending a number of foundational papers on classical obfuscation to the quantum setting. We prove that quantum black-box obfuscation is impossible in a setting where adversaries can possess more than one output of the obfuscator. In particular, generic transformation of quantum circuits into black-box-obfuscated quantum circuits is impossible. We also show that statistical indistinguishability obfuscation is impossible, up to an unlikely complexity-theoretic collapse. Our proofs involve a new tool: chosen-ciphertext-secure encryption of quantum data, which was recently shown to be possible assuming quantum-secure one-way functions exist [Alagic et al '16]. %8 2016/02/04 %G eng %U http://arxiv.org/abs/1602.01771 %0 Journal Article %J Quantum Information and Computation %D 2016 %T A Quantum Version of Schöning's Algorithm Applied to Quantum 2-SAT %A Edward Farhi %A Shelby Kimmel %A Kristan Temme %XWe study a quantum algorithm that consists of a simple quantum Markov process, and we analyze its behavior on restricted versions of Quantum 2-SAT. We prove that the algorithm solves this decision problem with high probability for n qubits, L clauses, and promise gap c in time O(n^2 L^2 c^{-2}). If the Hamiltonian is additionally polynomially gapped, our algorithm efficiently produces a state that has high overlap with the satisfying subspace. The Markov process we study is a quantum analogue of Sch\"oning's probabilistic algorithm for k-SAT.

%B Quantum Information and Computation %V 16 %8 2016/03/22 %G eng %U http://arxiv.org/abs/1603.06985 %N 13-14 %0 Journal Article %J Physical Review Letters %D 2016 %T Quantum-Enhanced Machine Learning %A Dunjko, Vedran %A Taylor, Jacob M. %A Briegel, Hans J. %XThe emerging field of quantum machine learning has the potential to substantially aid in the problems and scope of artificial intelligence. This is only enhanced by recent successes in the field of classical machine learning. In this work we propose an approach for the systematic treatment of machine learning, from the perspective of quantum information. Our approach is general and covers all three main branches of machine learning: supervised, unsupervised, and reinforcement learning. While quantum improvements in supervised and unsupervised learning have been reported, reinforcement learning has received much less attention. Within our approach, we tackle the problem of quantum enhancements in reinforcement learning as well, and propose a systematic scheme for providing improvements. As an example, we show that quadratic improvements in learning efficiency, and exponential improvements in performance over limited time periods, can be obtained for a broad class of learning problems.

%B Physical Review Letters %V 117 %P 130501 %8 2016/09/20 %G eng %U http://link.aps.org/doi/10.1103/PhysRevLett.117.130501 %N 13 %R 10.1103/PhysRevLett.117.130501 %0 Journal Article %D 2016 %T A quasi-mode theory of chiral phonons %A Xunnong Xu %A Seunghwi Kim %A Gaurav Bahl %A Jacob M. Taylor %XThe coherence properties of mechanical resonators are often limited by multiple unavoidable forms of loss -- including phonon-phonon and phonon-defect scattering -- which result in the scattering of sound into other resonant modes and into the phonon bath. Dynamic suppression of this scattering loss can lift constraints on device structure and can improve tolerance to defects in the material, even after fabrication. Inspired by recent experiments, here we introduce a model of phonon losses resulting from disorder in a whispering gallery mode resonator with acousto-optical coupling between optical and mechanical modes. We show that a typical elastic scattering mechanism of high quality factor (Q) mechanical modes flips the direction of phonon propagation via high-angle scattering, leading to damping into modes with the opposite parity. When the optical mode overlaps co-propagating high-Q and bulk mechanical modes, the addition of laser cooling via sideband-resolved damping of the mechanical mode of a chosen parity also damps and modifies the response of the bulk modes of the same parity. This, in turn, simultaneously improves the quality factor and reduces the thermal load of the counter-propagating high-Q modes, leading to the dynamical creation of a cold phononic shield. We compare our theoretical results to the recent experiments of Kim et al., and find quantitative agreement with our theory.

%8 2016/12/29 %G eng %U https://arxiv.org/abs/1612.09240 %0 Journal Article %J Physical Review A %D 2016 %T Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms %A Michael E. Beverland %A Gorjan Alagic %A Michael J. Martin %A Andrew P. Koller %A Ana M. Rey %A Alexey V. Gorshkov %XWe show that n thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the Sn symmetry that permutes atoms occupying different vibrational levels of the trap and the SU(N) symmetry associated with N nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU(N) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.

%B Physical Review A %V 93 %8 2016/05/06 %G eng %U http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.051601 %N 5 %R 10.1103/PhysRevA.93.051601 %0 Journal Article %J Journal of the ACM %D 2016 %T Robust Protocols for Securely Expanding Randomness and Distributing Keys Using Untrusted Quantum Devices %A Carl Miller %A Yaoyun Shi %K key distribution %K nonlocal games %K privacy %K quantum cryptography %K random-number generation %K untrusted device %XRandomness is a vital resource for modern-day information processing, especially for cryptography. A wide range of applications critically rely on abundant, high-quality random numbers generated securely. Here, we show how to expand a random seed at an exponential rate without trusting the underlying quantum devices. Our approach is secure against the most general adversaries, and has the following new features: cryptographic level of security, tolerating a constant level of imprecision in devices, requiring only unit size quantum memory (for each device component) in an honest implementation, and allowing a large natural class of constructions for the protocol. In conjunction with a recent work by Chung et al. [2014], it also leads to robust unbounded expansion using just 2 multipart devices. When adapted for distributing cryptographic keys, our method achieves, for the first time, exponential expansion combined with cryptographic security and noise tolerance. The proof proceeds by showing that the Rényi divergence of the outputs of the protocol (for a specific bounding operator) decreases linearly as the protocol iterates. At the heart of the proof are a new uncertainty principle on quantum measurements and a method for simulating trusted measurements with untrusted devices.

%B Journal of the ACM %V 63 %P 33:1–33:63 %8 2016/10/26 %G eng %U http://doi.acm.org/10.1145/2885493 %N 4 %R 10.1145/2885493 %0 Journal Article %J Physical Review A %D 2016 %T Self-organization of atoms coupled to a chiral reservoir %A Zachary Eldredge %A Pablo Solano %A Darrick Chang %A Alexey V. Gorshkov %XTightly confined modes of light, as in optical nanofibers or photonic crystal waveguides, can lead to large optical coupling in atomic systems, which mediates long-range interactions between atoms. These one-dimensional systems can naturally possess couplings that are asymmetric between modes propagating in different directions. Strong long-range interaction among atoms via these modes can drive them to a self-organized periodic distribution. In this paper, we examine the self-organizing behavior of atoms in one dimension coupled to a chiral reservoir. We determine the solution to the equations of motion in different parameter regimes, relative to both the detuning of the pump laser that initializes the atomic dipole-dipole interactions and the degree of reservoir chirality. In addition, we calculate possible experimental signatures such as reflectivity from self-organized atoms and motional sidebands.

%B Physical Review A %V 94 %P 053855 %8 2016/11/29 %G eng %U http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.053855 %N 5 %R 10.1103/PhysRevA.94.053855 %0 Journal Article %J New Journal of Physics %D 2016 %T Serialized Quantum Error Correction Protocol for High-Bandwidth Quantum Repeaters %A Andrew N. Glaudell %A Edo Waks %A Jacob M. Taylor %XAdvances in single photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have losses low enough to be correctable using a quantum error correcting code. Such error-corrected communication is equivalent to a novel quantum repeater scheme, but crucial questions regarding implementation and system requirements remain open. Here we show that long range entangled bit generation with rates approaching $10^8$ ebits/s may be possible using a completely serialized protocol, in which photons are generated, entangled, and error corrected via sequential, one-way interactions with a minimal number of matter qubits. Provided loss and error rates of the required elements are below the threshold for quantum error correction, this scheme demonstrates improved performance over transmission of single photons. We find improvement in ebit rates at large distances using this serial protocol and various quantum error correcting codes.

%B New Journal of Physics %V 18 %P 093008 %8 2016/09/02 %G eng %U http://iopscience.iop.org/article/10.1088/1367-2630/18/9/093008/meta %N 9 %R 10.1088/1367-2630/18/9/093008 %0 Journal Article %J Physical Review Letters %D 2016 %T Sisyphus Thermalization of Photons in a Cavity-Coupled Double Quantum Dot %A Michael Gullans %A J. Stehlik %A Y. -Y. Liu %A J. R. Petta %A J. M. Taylor %XA strongly driven quantum system, coupled to a thermalizing bath, generically evolves into a highly non-thermal state as the external drive competes with the equilibrating force of the bath. We demonstrate a notable exception to this picture for a microwave resonator interacting with a periodically driven double quantum dot (DQD). In the limit of strong driving and long times, we show that the resonator field can be driven into a thermal state with a chemical potential given by a harmonic of the drive frequency. Such tunable chemical potentials are achievable with current devices and would have broad utility for quantum simulation in circuit quantum electrodynamics. As an example, we show how several DQDs embedded in an array of microwave resonators can induce a phase transition to a Bose-Einstein condensate of light.

%B Physical Review Letters %V 117 %P 056801 %8 2016/07/25 %G eng %U http://arxiv.org/abs/1512.01248 %N 5 %R http://dx.doi.org/10.1103/PhysRevLett.117.056801 %0 Journal Article %J 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) %D 2016 %T Space-Efficient Error Reduction for Unitary Quantum Computations %A Bill Fefferman %A Hirotada Kobayashi %A Cedric Yen-Yu Lin %A Tomoyuki Morimae %A Harumichi Nishimura %XThis paper develops general space-efficient methods for error reduction for unitary quantum computation. Consider a polynomial-time quantum computation with completeness

A steady-state superradiant laser can be used to generate ultranarrow-linewidth light, and thus has important applications in the fields of quantum information and precision metrology. However, the light produced by such a laser is still essentially classical. Here, we show that the introduction of a Rydberg medium into a cavity containing atoms with a narrow optical transition can lead to the steady-state superradiant emission of ultranarrow-linewidth

We propose a method for creating far-field optical barrier potentials for ultracold atoms with widths that are narrower than the diffraction limit and can approach tens of nanometers. The reduced widths stem from the nonlinear atomic response to control fields that create spatially varying dark resonances. The subwavelength barrier is the result of the geometric scalar potential experienced by an atom prepared in such a spatially varying dark state. The performance of this technique, as well as its applications to the study of many-body physics and to the implementation of quantum-information protocols with ultracold atoms, are discussed, with a focus on the implementation of tunnel junctions.

%B Physical Review A %V 94 %P 063422 %8 2016/12/27 %G eng %U http://link.aps.org/doi/10.1103/PhysRevA.94.063422 %N 6 %R 10.1103/PhysRevA.94.063422 %0 Journal Article %J Physical Review A %D 2016 %T Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices %A Marlon Nuske %A L. Mathey %A Eite Tiesinga %XWe determine the exact time evolution of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultra-cold atoms in a hexagonal optical lattice. The dynamical evolution is triggered by ramping the lattice potential up, such that the interaction strength Uf is much larger than the hopping amplitude Jf. The quench initiates collective oscillations with frequency |Uf|/(2π) in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the order parameter Δ. The latter is not reproduced by treating the time evolution in mean-field theory. The momentum density-density or noise correlation functions oscillate at frequency |Uf|/2π as well as its second harmonic. For a very deep lattice, with negligible tunneling energy, the oscillations of momentum occupation numbers are undamped. Non-zero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. This occurs even for a finite-temperature initial BCS state, but not for a non-interacting Fermi gas. We therefore propose to use this dephasing to detect a BCS state. Finally, we predict that the noise correlation functions in a honeycomb lattice will develop strong anti-correlations near the Dirac point.

%B Physical Review A %V 94 %P 023607 %8 2016/08/05 %G eng %U http://arxiv.org/abs/1602.00979 %N 2 %R http://dx.doi.org/10.1103/PhysRevA.94.023607 %0 Journal Article %J Physical Review Letters %D 2016 %T Tomography is necessary for universal entanglement detection with single-copy observables %A Dawei Lu %A Tao Xin %A Nengkun Yu %A Zhengfeng Ji %A Jianxin Chen %A Guilu Long %A Jonathan Baugh %A Xinhua Peng %A Bei Zeng %A Raymond Laflamme %X Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. By performing the experiment and analyzing the data, we demonstrate that the information gathered is indeed sufficient to reconstruct the state. These results reveal a fundamental limit for single-copy measurements in entanglement detection, and provides a general framework to study the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility. %B Physical Review Letters %V 116 %P 230501 %8 2016/06/07 %G eng %U http://arxiv.org/abs/1511.00581 %N 23 %R 10.1103/PhysRevLett.116.230501 %0 Journal Article %J Physical Review B %D 2016 %T Topological phases with long-range interactions %A Zhe-Xuan Gong %A Mohammad F. Maghrebi %A Anzi Hu %A Michael L. Wall %A Michael Foss-Feig %A Alexey V. Gorshkov %X Topological phases of matter are primarily studied in quantum many-body systems with short-range interactions. Whether various topological phases can survive in the presence of long-range interactions, however, is largely unknown. Here we show that a paradigmatic example of a symmetry-protected topological phase, the Haldane phase of an antiferromagnetic spin-1 chain, surprisingly remains intact in the presence of arbitrarily slowly decaying power-law interactions. The influence of long-range interactions on the topological order is largely quantitative, and we expect similar results for more general systems. Our conclusions are based on large-scale matrix-product-state simulations and two complementary effective-field-theory calculations. The striking agreement between the numerical and analytical results rules out finite-size effects. The topological phase considered here should be experimentally observable in a recently developed trapped-ion quantum simulator. %B Physical Review B %V 93 %P 041102 %8 2016/01/08 %G eng %U http://arxiv.org/abs/1505.03146 %N 4 %R 10.1103/PhysRevB.93.041102 %0 Journal Article %J Theory of Computing %D 2016 %T Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman bomb tester %A Cedric Yen-Yu Lin %A Han-Hsuan Lin %XInspired by the Elitzur-Vaidman bomb testing problem [arXiv:hep-th/9305002], we introduce a new query complexity model, which we call bomb query complexity $B(f)$. We investigate its relationship with the usual quantum query complexity $Q(f)$, and show that $B(f)=\Theta(Q(f)^2)$. This result gives a new method to upper bound the quantum query complexity: we give a method of finding bomb query algorithms from classical algorithms, which then provide nonconstructive upper bounds on $Q(f)=\Theta(\sqrt{B(f)})$. We subsequently were able to give explicit quantum algorithms matching our upper bound method. We apply this method on the single-source shortest paths problem on unweighted graphs, obtaining an algorithm with $O(n^{1.5})$ quantum query complexity, improving the best known algorithm of $O(n^{1.5}\sqrt{\log n})$ [arXiv:quant-ph/0606127]. Applying this method to the maximum bipartite matching problem gives an $O(n^{1.75})$ algorithm, improving the best known trivial $O(n^2)$ upper bound.

%B Theory of Computing %V 12 %P 1-35 %8 2016/11/28 %G eng %U http://theoryofcomputing.org/articles/v012a018/ %N 18 %( Proceeding CCC '15 Proceedings of the 30th Conference on Computational Complexity, Pages 537-566 %R 10.4086/toc.2016.v012a018 %0 Journal Article %J Physical Review A %D 2016 %T Wannier functions using a discrete variable representation for optical lattices %A Saurabh Paul %A Eite Tiesinga %XWe propose a numerical method using the discrete variable representation (DVR) for constructing real-valued Wannier functions localized in a unit cell for both symmetric and asymmetric periodic potentials. We apply these results to finding Wannier functions for ultracold atoms trapped in laser-generated optical lattices. Following S. Kivelson [Phys. Rev. B 26, 4269 (1982)], for a symmetric lattice with inversion symmetry, we construct Wannier functions as eigenstates of the position operators

Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, achieving tunable, coherent long-range interactions between atoms is an outstanding challenge, which currently leaves a large class of models inaccessible to quantum simulation. Here, we propose a solution exploiting the powerful new platform of cold atoms trapped near nano-photonic systems. We show that the dielectric contrast of an atom trapped near a photonic crystal can seed a localized cavity mode around the atomic position. In a dynamic form of “all-atomic” cavity QED, the length of these cavity modes can be tuned, and atoms separated by the order of the e↵ective cavity length can interact coherently with each other. Considering realistic conditions such as fabrication disorder and photon losses, coherent long-range potentials or spin interactions can be dominant in the system over length scales up to hundreds of wavelengths.

%B Nature Photon. 9, 326 (2015) %8 2015/03/03 %G eng %U http://www.nature.com/nphoton/journal/v9/n5/full/nphoton.2015.57.html %R doi:10.1038/nphoton.2015.57 %0 Journal Article %J Physical Review A %D 2015 %T Bilayer fractional quantum Hall states with ultracold dysprosium %A Norman Y. Yao %A Steven D. Bennett %A Chris R. Laumann %A Benjamin L. Lev %A Alexey V. Gorshkov %X We show how dipolar interactions between dysprosium atoms in an optical lattice can be used to obtain fractional quantum Hall states. In our approach, dysprosium atoms are trapped one atom per site in a deep optical lattice with negligible tunneling. Microwave and spatially dependent optical dressing fields are used to define an effective spin-1/2 or spin-1 degree of freedom in each atom. Thinking of spin-1/2 particles as hardcore bosons, dipole-dipole interactions give rise to boson hopping, topological flat bands with Chern number 1, and the \nu = 1/2 Laughlin state. Thinking of spin-1 particles as two-component hardcore bosons, dipole-dipole interactions again give rise to boson hopping, topological flat bands with Chern number 2, and the bilayer Halperin (2,2,1) state. By adjusting the optical fields, we find a phase diagram, in which the (2,2,1) state competes with superfluidity. Generalizations to solid-state magnetic dipoles are discussed. %B Physical Review A %V 92 %P 033609 %8 2015/09/10 %G eng %U http://arxiv.org/abs/1505.03099v1 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.92.033609 %0 Journal Article %J New Journal of Physics %D 2015 %T Bounds on quantum communication via Newtonian gravity %A D. Kafri %A G. J. Milburn %A J. M. Taylor %X Newtonian gravity yields specific observable consequences, the most striking of which is the emergence of a $1/r^2$ force. In so far as communication can arise via such interactions between distant particles, we can ask what would be expected for a theory of gravity that only allows classical communication. Many heuristic suggestions for gravity-induced decoherence have this restriction implicitly or explicitly in their construction. Here we show that communication via a $1/r^2$ force has a minimum noise induced in the system when the communication cannot convey quantum information, in a continuous time analogue to Bell's inequalities. Our derived noise bounds provide tight constraints from current experimental results on any theory of gravity that does not allow quantum communication. %B New Journal of Physics %V 17 %P 015006 %8 2015/01/15 %G eng %U http://arxiv.org/abs/1404.3214v2 %N 1 %! New J. Phys. %R 10.1088/1367-2630/17/1/015006 %0 Journal Article %J Physical Review B %D 2015 %T Capacitively coupled singlet-triplet qubits in the double charge resonant regime %A V. Srinivasa %A J. M. Taylor %X We investigate a method for entangling two singlet-triplet qubits in adjacent double quantum dots via capacitive interactions. In contrast to prior work, here we focus on a regime with strong interactions between the qubits. The interplay of the interaction energy and simultaneous large detunings for both double dots gives rise to the double charge resonant regime, in which the unpolarized (1111) and fully polarized (0202) four-electron states in the absence of interqubit tunneling are near degeneracy, while being energetically well-separated from the partially polarized (0211 and 1102) states. A controlled-phase gate may be realized by combining time evolution in this regime in the presence of intraqubit tunneling and the interqubit Coulomb interaction with refocusing {\pi} pulses that swap the singly occupied singlet and triplet states of the two qubits via, e.g., magnetic gradients. We calculate the fidelity of this entangling gate, incorporating models for two types of noise - classical, Gaussian-distributed charge fluctuations in the single-qubit detunings and charge relaxation within the low-energy subspace via electron-phonon interaction - and identify parameter regimes that optimize the fidelity. The rates of phonon-induced decay for pairs of GaAs or Si double quantum dots vary with the sizes of the dipolar and quadrupolar contributions and are several orders of magnitude smaller for Si, leading to high theoretical gate fidelities for coupled singlet-triplet qubits in Si dots. We also consider the dependence of the capacitive coupling on the relative orientation of the double dots and find that a linear geometry provides the fastest potential gate. %B Physical Review B %V 92 %P 235301 %8 2015/12/01 %G eng %U http://arxiv.org/abs/1408.4740v2 %N 23 %0 Journal Article %J Physical Review B %D 2015 %T A chemical potential for light %A M. Hafezi %A P. Adhikari %A J. M. Taylor %X Photons are not conserved in interactions with other matter. Consequently, when understanding the equation of state and thermodynamics of photons, while we have a concept of temperature for energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in understanding a wide variety of single- and many-body effects, from transport in conductors and semi-conductors to phase transitions in electronic and atomic systems. Here we show how a direct modification of the system-bath coupling via parametric oscillation creates an effective chemical potential for photons even in the thermodynamic limit. Specific implementations, using circuit-QED or optomechanics, are feasible using current technologies, and we show a detailed example demonstrating the emergence of Mott Insulator-superfluid transition in a lattice of nonlinear oscillators. Our approach paves the way for quantum simulation, quantum sources and even electron-like circuits with light. %B Physical Review B %V 92 %P 174305 %8 2014/05/22 %G eng %U http://arxiv.org/abs/1405.5821v2 %N 17 %R 10.1103/PhysRevB.92.174305 %0 Journal Article %D 2015 %T Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems %A Mohammad F. Maghrebi %A Zhe-Xuan Gong %A Alexey V. Gorshkov %X Continuous symmetry breaking (CSB) in low-dimensional systems, forbidden by the Mermin-Wagner theorem for short-range interactions, may take place in the presence of slowly decaying long-range interactions. Nevertheless, there is no stringent bound on how slowly interactions should decay to give rise to CSB in 1D quantum systems at zero temperature. Here, we study a long-range interacting spin chain with U(1) symmetry and power-law interactions V(r)∼1/rα, directly relevant to ion-trap experiments. Using bosonization and renormalization group theory, we find CSB for α smaller than a critical exponent αc(≤3) depending on the microscopic parameters of the model. Furthermore, the transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal symmetry due to long-range interactions, and is described by a new universality class akin to the Berezinskii-Kosterlitz-Thouless transition. Our analytical findings are in good agreement with a numerical calculation. Signatures of the CSB phase should be accessible in existing trapped-ion experiments. %8 2015/10/05 %G eng %U http://arxiv.org/abs/1510.01325 %0 Journal Article %J Physical Review Letters %D 2015 %T Coulomb bound states of strongly interacting photons %A Mohammad F. Maghrebi %A Michael Gullans %A P. Bienias %A S. Choi %A I. Martin %A O. Firstenberg %A M. D. Lukin %A H. P. Büchler %A Alexey V. Gorshkov %X We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasi-bound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wavefunction resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms. %B Physical Review Letters %V 115 %P 123601 %8 2015/09/16 %G eng %U http://arxiv.org/abs/1505.03859v1 %N 12 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.115.123601 %0 Journal Article %J New Journal of Physics %D 2015 %T Demonstration of Robust Quantum Gate Tomography via Randomized Benchmarking %A Blake R. Johnson %A Marcus P. da Silva %A Colm A. Ryan %A Shelby Kimmel %A Jerry M. Chow %A Thomas A. Ohki %X Typical quantum gate tomography protocols struggle with a self-consistency problem: the gate operation cannot be reconstructed without knowledge of the initial state and final measurement, but such knowledge cannot be obtained without well-characterized gates. A recently proposed technique, known as randomized benchmarking tomography (RBT), sidesteps this self-consistency problem by designing experiments to be insensitive to preparation and measurement imperfections. We implement this proposal in a superconducting qubit system, using a number of experimental improvements including implementing each of the elements of the Clifford group in single `atomic' pulses and custom control hardware to enable large overhead protocols. We show a robust reconstruction of several single-qubit quantum gates, including a unitary outside the Clifford group. We demonstrate that RBT yields physical gate reconstructions that are consistent with fidelities obtained by randomized benchmarking. %B New Journal of Physics %V 17 %P 113019 %8 2015/11/05 %G eng %U http://arxiv.org/abs/1505.06686 %N 11 %R 10.1088/1367-2630/17/11/113019 %0 Journal Article %J New Journal of Physics %D 2015 %T Discontinuity of Maximum Entropy Inference and Quantum Phase Transitions %A Jianxin Chen %A Zhengfeng Ji %A Chi-Kwong Li %A Yiu-Tung Poon %A Yi Shen %A Nengkun Yu %A Bei Zeng %A Duanlu Zhou %X In this paper, we discuss the connection between two genuinely quantum phenomena --- the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit. %B New Journal of Physics %V 17 %P 083019 %8 2015/08/10 %G eng %U http://arxiv.org/abs/1406.5046v2 %N 8 %! New J. Phys. %R 10.1088/1367-2630/17/8/083019 %0 Journal Article %J Physical Review Letters %D 2015 %T Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension %A Mohammad F. Maghrebi %A Homer Reid %X A dispersive medium becomes entangled with zero-point fluctuations in the vacuum. We consider an arbitrary array of material bodies weakly interacting with a quantum field and compute the quantum mutual information between them. It is shown that the mutual information in D dimensions can be mapped to classical thermodynamic entropy in D+1 dimensions. As a specific example, we compute the mutual information both analytically and numerically for a range of separation distances between two bodies in D=2 dimensions and find a logarithmic correction to the area law at short separations. A key advantage of our method is that it allows the strong subadditivity property---notoriously difficult to prove for quantum systems---to be easily verified. %B Physical Review Letters %V 114 %P 151602 %8 2015/04/16 %G eng %U http://arxiv.org/abs/1412.5613v2 %N 15 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.114.151602 %0 Journal Article %J Nature %D 2015 %T Entangling two transportable neutral atoms via local spin exchange %A A. M. Kaufman %A B. J. Lester %A Michael Foss-Feig %A M. L. Wall %A A. M. Rey %A C. A. Regal %X To advance quantum information science a constant pursuit is the search for physical systems that meet the stringent requirements for creating and preserving quantum entanglement. In atomic physics, robust two-qubit entanglement is typically achieved by strong, long-range interactions in the form of Coulomb interactions between ions or dipolar interactions between Rydberg atoms. While these interactions allow fast gates, atoms subject to these interactions must overcome the associated coupling to the environment and cross-talk among qubits. Local interactions, such as those requiring significant wavefunction overlap, can alleviate these detrimental effects yet present a new challenge: To distribute entanglement, qubits must be transported, merged for interaction, and then isolated for storage and subsequent operations. Here we show how, via a mobile optical tweezer, it is possible to prepare and locally entangle two ultracold neutral atoms, and then separate them while preserving their entanglement. While ultracold neutral atom experiments have measured dynamics consistent with spin entanglement, we are now able to demonstrate two-particle coherence via application of a local gradient and parity measurements; this new entanglement-verification protocol could be applied to arbitrary spin-entangled states of spatially-separated atoms. The local entangling operation is achieved via ultracold spin-exchange interactions, and quantum tunneling is used to combine and separate atoms. Our toolset provides a framework for dynamically entangling remote qubits via local operations within a large-scale quantum register. %B Nature %V 527 %P 208-211 %8 2015/11/02 %G eng %U http://arxiv.org/abs/1507.05586 %R 10.1038/nature16073 %0 Journal Article %J Physical Review A %D 2015 %T Fractional Quantum Hall States of Rydberg Polaritons %A Mohammad F. Maghrebi %A Norman Y. Yao %A Mohammad Hafezi %A Thomas Pohl %A Ofer Firstenberg %A Alexey V. Gorshkov %X We propose a scheme for realizing fractional quantum Hall states of light. In our scheme, photons of two polarizations are coupled to different atomic Rydberg states to form two flavors of Rydberg polaritons that behave as an effective spin. An array of optical cavity modes overlapping with the atomic cloud enables the realization of an effective spin-1/2 lattice. We show that the dipolar interaction between such polaritons, inherited from the Rydberg states, can be exploited to create a flat, topological band for a single spin-flip excitation. At half filling, this gives rise to a photonic (or polaritonic) fractional Chern insulator -- a lattice-based, fractional quantum Hall state of light. %B Physical Review A %V 91 %P 033838 %8 2015/03/31 %G eng %U http://arxiv.org/abs/1411.6624v1 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.91.033838 %0 Journal Article %D 2015 %T Framework for learning agents in quantum environments %A Vedran Dunjko %A J. M. Taylor %A Hans J. Briegel %X In this paper we provide a broad framework for describing learning agents in general quantum environments. We analyze the types of classically specified environments which allow for quantum enhancements in learning, by contrasting environments to quantum oracles. We show that whether or not quantum improvements are at all possible depends on the internal structure of the quantum environment. If the environments are constructed and the internal structure is appropriately chosen, or if the agent has limited capacities to influence the internal states of the environment, we show that improvements in learning times are possible in a broad range of scenarios. Such scenarios we call luck-favoring settings. The case of constructed environments is particularly relevant for the class of model-based learning agents, where our results imply a near-generic improvement. %8 2015/07/30 %G eng %U http://arxiv.org/abs/1507.08482v1 %0 Journal Article %J Annalen der Physik %D 2015 %T From membrane-in-the-middle to mirror-in-the-middle with a high-reflectivity sub-wavelength grating %A Corey Stambaugh %A Haitan Xu %A Utku Kemiktarak %A J. M. Taylor %A John Lawall %X We demonstrate a "membrane in the middle" optomechanical system using a silicon nitride membrane patterned as a subwavelength grating. The grating has a reflectivity of over 99.8%, effectively creating two sub-cavities, with free spectral ranges of 6 GHz, optically coupled via photon tunneling. Measurements of the transmission and reflection spectra show an avoided crossing where the two sub-cavities simultaneously come into resonance, with a frequency splitting of 54 MHz. We derive expressions for the lineshapes of the symmetric and antisymmetric modes at the avoided crossing, and infer the grating reflection, transmission, absorption, and scattering through comparison with the experimental data. %B Annalen der Physik %V 527 %P 81 - 88 %8 2015/01/02 %G eng %U http://arxiv.org/abs/1407.1709v1 %N 1-2 %! ANNALEN DER PHYSIK %R 10.1002/andp.201400142 %0 Journal Article %J Proceedings of the 56th IEEE Symposium on Foundations of Computer Science %D 2015 %T Hamiltonian simulation with nearly optimal dependence on all parameters %A Dominic W. Berry %A Andrew M. Childs %A Robin Kothari %X We present an algorithm for sparse Hamiltonian simulation that has optimal dependence on all parameters of interest (up to log factors). Previous algorithms had optimal or near-optimal scaling in some parameters at the cost of poor scaling in others. Hamiltonian simulation via a quantum walk has optimal dependence on the sparsity $d$ at the expense of poor scaling in the allowed error $\epsilon$. In contrast, an approach based on fractional-query simulation provides optimal scaling in $\epsilon$ at the expense of poor scaling in $d$. Here we combine the two approaches, achieving the best features of both. By implementing a linear combination of quantum walk steps with coefficients given by Bessel functions, our algorithm achieves near-linear scaling in $\tau := d \|H\|_{\max} t$ and sublogarithmic scaling in $1/\epsilon$. Our dependence on $\epsilon$ is optimal, and we prove a new lower bound showing that no algorithm can have sublinear dependence on $\tau$. %B Proceedings of the 56th IEEE Symposium on Foundations of Computer Science %P 792-809 %8 2015/01/08 %G eng %U http://arxiv.org/abs/1501.01715 %R 10.1109/FOCS.2015.54 %0 Journal Article %J Physical Review A %D 2015 %T Injection Locking of a Semiconductor Double Quantum Dot Micromaser %A Y. -Y. Liu %A J. Stehlik %A Michael Gullans %A J. M. Taylor %A J. R. Petta %X Emission linewidth is an important figure of merit for masers and lasers. We recently demonstrated a semiconductor double quantum dot (DQD) micromaser where photons are generated through single electron tunneling events. Charge noise directly couples to the DQD energy levels, resulting in a maser linewidth that is more than 100 times larger than the Schawlow-Townes prediction. Here we demonstrate a linewidth narrowing of more than a factor 10 by locking the DQD emission to a coherent tone that is injected to the input port of the cavity. We measure the injection locking range as a function of cavity input power and show that it is in agreement with the Adler equation. The position and amplitude of distortion sidebands that appear outside of the injection locking range are quantitatively examined. Our results show that this unconventional maser, which is impacted by strong charge noise and electron-phonon coupling, is well described by standard laser models. %B Physical Review A %V 92 %P 053802 %8 2015/11/02 %G eng %U http://arxiv.org/abs/1508.04147 %N 5 %R 10.1103/PhysRevA.92.053802 %0 Journal Article %J Linear Algebra and its Applications %D 2015 %T Laplacian matrices and Alexandrov topologies of digraphs %A Aaron Ostrander %K Laplacian matrix %X We explore the spectral properties of digraph Laplacians and how they relate to topological properties of digraphs (such as openness, closure, and strong connectedness) under the Alexandrov topology. %B Linear Algebra and its Applications %V 481 %P 174 - 185 %8 2015/09/15 %G eng %U http://www.sciencedirect.com/science/article/pii/S0024379515002840 %R http://dx.doi.org/10.1016/j.laa.2015.04.031 %0 Journal Article %J Phys. Rev. A 92, 023602 %D 2015 %T Large effective three-body interaction in a double-well optical lattice %A Saurabh Paul %A Eite Tiesinga %X We study ultracold atoms in an optical lattice with two local minima per unit cell and show that the low energy states of a multi-band Bose-Hubbard (BH) Hamiltonian with only pair-wise interactions is equivalent to an effective single-band Hamiltonian with strong three-body interactions. We focus on a double-well optical lattice with a symmetric double well along the $x$ axis and single well structure along the perpendicular directions. Tunneling and two-body interaction energies are obtained from an exact band-structure calculation and numerically-constructed Wannier functions in order to construct a BH Hamiltonian spanning the lowest two bands. Our effective Hamiltonian is constructed from the ground state of the $N$-atom Hamiltonian for each unit cell obtained within the subspace spanned by the Wannier functions of two lowest bands. The model includes hopping between ground states of neighboring unit cells. We show that such an effective Hamiltonian has strong three-body interactions that can be easily tuned by changing the lattice parameters. Finally, relying on numerical mean-field simulations, we show that the effective Hamiltonian is an excellent approximation of the two-band BH Hamiltonian over a wide range of lattice parameters, both in the superfluid and Mott insulator regions. %B Phys. Rev. A 92, 023602 %V 92 %P 023602 %8 2015/08/03 %G eng %U http://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.023602 %N 2 %0 Journal Article %J Entropy %D 2015 %T The Measurement Problem from the Perspective of an Information Theoretic Interpretation of Quantum Mechanics %A Jeffrey Bub %X The aim of this paper is to consider the consequences of an information-theoretic interpretation of quantum mechanics for the measurement problem. The motivating idea of the interpretation is that the relation between quantum mechanics and the structure of information is analogous to the relation between special relativity and the structure of space-time. Insofar as quantum mechanics deals with a class of probabilistic correlations that includes correlations structurally different from classical correlations, the theory is about the structure of information: the possibilities for representing, manipulating, and communicating information in a genuinely indeterministic quantum world in which measurement outcomes are intrinsically random are different than we thought. Part of the measurement problem is deflated as a pseudo-problem on this view, and the theory has the resources to deal with the remaining part, given certain idealizations in the treatment of macrosystems. %B Entropy %V 17 %P 7374-7386 %8 10/28/2015 %G eng %U http://www.mdpi.com/1099-4300/17/11/7374 %N 11 %R 10.3390/e17117374 %0 Journal Article %J Communications in Mathematical Physics %D 2015 %T The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases) %A Jianxin Chen %A Nathaniel Johnston %X A long-standing open question asks for the minimum number of vectors needed to form an unextendible product basis in a given bipartite or multipartite Hilbert space. A partial solution was found by Alon and Lovasz in 2001, but since then only a few other cases have been solved. We solve all remaining bipartite cases, as well as a large family of multipartite cases. %B Communications in Mathematical Physics %V 333 %P 351 - 365 %8 2014/10/10 %G eng %U http://arxiv.org/abs/1301.1406v1 %N 1 %! Commun. Math. Phys. %R 10.1007/s00220-014-2186-7 %0 Journal Article %J Quantum Information and Computation %D 2015 %T Momentum switches %A Andrew M. Childs %A David Gosset %A Daniel Nagaj %A Mouktik Raha %A Zak Webb %X Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior. In this paper, we study and construct momentum switches, graphs that route particles depending on their momenta. We also give an example where there is no exact momentum switch, although we construct an arbitrarily good approximation. %B Quantum Information and Computation %V 15 %P 601-621 %8 2015/05/01 %G eng %U http://arxiv.org/abs/1406.4510v1 %N 7-8 %! Quantum Information and Computation 15 %0 Journal Article %J Physical Review Letters %D 2015 %T Nearly-linear light cones in long-range interacting quantum systems %A Michael Foss-Feig %A Zhe-Xuan Gong %A Charles W. Clark %A Alexey V. Gorshkov %X In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/r^{\alpha}$) interactions, when $\alpha$ exceeds the dimension $D$, an analogous bound confines influences to within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are algebraic for $\alpha>2D$, becoming linear as $\alpha\rightarrow\infty$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems. %B Physical Review Letters %V 114 %P 157201 %8 2015/04/13 %G eng %U http://arxiv.org/abs/1410.3466v1 %N 15 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.114.157201 %0 Journal Article %D 2015 %T Observation of optomechanical buckling phase transitions %A Haitan Xu %A Utku Kemiktarak %A Jingyun Fan %A Stephen Ragole %A John Lawall %A Jacob M. Taylor %XCorrelated phases of matter provide long-term stability for systems as diverse as solids, magnets, and potential exotic quantum materials. Mechanical systems, such as relays and buckling transition spring switches can yield similar stability by exploiting non-equilibrium phase transitions. Curiously, in the optical domain, observations of such phase transitions remain elusive. However, efforts to integrate optical and mechanical systems -- optomechanics -- suggest that a hybrid approach combining the quantum control of optical systems with the engineerability of mechanical systems may provide a new avenue for such explorations. Here we report the first observation of the buckling of an optomechanical system, in which transitions between stable mechanical states corresponding to both first- and second-order phase transitions are driven by varying laser power and detuning. Our results enable new applications in photonics and, given rapid progress in pushing optomechanical systems into the quantum regime, the potential for explorations of quantum phase transitions.

%8 2015/10/16 %G eng %U http://arxiv.org/abs/1510.04971v1 %0 Journal Article %J Physical Review B %D 2015 %T Optical Control of Donor Spin Qubits in Silicon %A Michael Gullans %A J. M. Taylor %X We show how to achieve optical, spin-selective transitions from the ground state to excited orbital states of group-V donors (P, As, Sb, Bi) in silicon. We consider two approaches based on either resonant, far-infrared (IR) transitions of the neutral donor or resonant, near-IR excitonic transitions. For far-IR light, we calculate the dipole matrix elements between the valley-orbit and spin-orbit split states for all the goup-V donors using effective mass theory. We then calculate the maximum rate and amount of electron-nuclear spin-polarization achievable through optical pumping with circularly polarized light. We find this approach is most promising for Bi donors due to their large spin-orbit and valley-orbit interactions. Using near-IR light, spin-selective excitation is possible for all the donors by driving a two-photon $\Lambda$-transition from the ground state to higher orbitals with even parity. We show that externally applied electric fields or strain allow similar, spin-selective $\Lambda$-transition to odd-parity excited states. We anticipate these results will be useful for future spectroscopic investigations of donors, quantum control and state preparation of donor spin qubits, and for developing a coherent interface between donor spin qubits and single photons. %B Physical Review B %V 92 %P 195411 %8 2015/11/11 %G eng %U http://arxiv.org/abs/1507.07929 %N 19 %R 10.1103/PhysRevB.92.195411 %0 Journal Article %J Quantum Information and Computation %D 2015 %T Optimal ancilla-free Clifford+V approximation of z-rotations %A Neil J. Ross %X We describe a new efficient algorithm to approximate z-rotations by ancilla-free Clifford+V circuits, up to a given precision epsilon. Our algorithm is optimal in the presence of an oracle for integer factoring: it outputs the shortest Clifford+V circuit solving the given problem instance. In the absence of such an oracle, our algorithm is still near-optimal, producing circuits of V-count m + O(log(log(1/epsilon))), where m is the V-count of the third-to-optimal solution. A restricted version of the algorithm approximates z-rotations in the Pauli+V gate set. Our method is based on previous work by the author and Selinger on the optimal ancilla-free approximation of z-rotations using Clifford+T gates and on previous work by Bocharov, Gurevich, and Svore on the asymptotically optimal ancilla-free approximation of z-rotations using Clifford+V gates. %B Quantum Information and Computation %V 15 %P 932-950 %8 2015/03/06 %G eng %U http://arxiv.org/abs/1409.4355v2 %N 11-12 %0 Journal Article %J Physical Review A %D 2015 %T Optimization of collisional Feshbach cooling of an ultracold nondegenerate gas %A Marlon Nuske %A Eite Tiesinga %A L. Mathey %X We optimize a collision-induced cooling process for ultracold atoms in the nondegenerate regime. It makes use of a Feshbach resonance, instead of rf radiation in evaporative cooling, to selectively expel hot atoms from a trap. Using functional minimization we analytically show that for the optimal cooling process the resonance energy must be tuned such that it linearly follows the temperature. Here, optimal cooling is defined as maximizing the phase-space density after a fixed cooling duration. The analytical results are confirmed by numerical Monte-Carlo simulations. In order to simulate more realistic experimental conditions, we show that background losses do not change our conclusions, while additional non-resonant two-body losses make a lower initial resonance energy with non-linear dependence on temperature preferable. %B Physical Review A %V 91 %P 043626 %8 2015/04/20 %G eng %U http://arxiv.org/abs/1412.8473v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.91.043626 %0 Journal Article %J Metrologia %D 2015 %T Optomechanical reference accelerometer %A Oliver Gerberding %A Felipe Guzman Cervantes %A John Melcher %A Jon R. Pratt %A J. M. Taylor %XWe present an optomechanical accelerometer with high dynamic range, high bandwidth and read-out noise levels below 8 ${\mu}$g/$\sqrt{\mathrm{Hz}}$. The straightforward assembly and low cost of our device make it a prime candidate for on-site reference calibrations and autonomous navigation. We present experimental data taken with a vacuum sealed, portable prototype and deduce the achieved bias stability and scale factor accuracy. Additionally, we present a comprehensive model of the device physics that we use to analyze the fundamental noise sources and accuracy limitations of such devices.

%B Metrologia %V 52 %P 654 %8 2015/09/08 %G eng %U http://iopscience.iop.org/article/10.1088/0026-1394/52/5/654/meta;jsessionid=C2B417A5CD50B9B57EE14C78E1783802.ip-10-40-1-105 %N 5 %R 10.1088/0026-1394/52/5/654 %0 Journal Article %J 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015) %D 2015 %T Oracles with Costs %A Shelby Kimmel %A Cedric Yen-Yu Lin %A Han-Hsuan Lin %X While powerful tools have been developed to analyze quantum query complexity, there are still many natural problems that do not fit neatly into the black box model of oracles. We create a new model that allows multiple oracles with differing costs. This model captures more of the difficulty of certain natural problems. We test this model on a simple problem, Search with Two Oracles, for which we create a quantum algorithm that we prove is asymptotically optimal. We further give some evidence, using a geometric picture of Grover's algorithm, that our algorithm is exactly optimal. %B 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015) %V 44 %P 1-26 %8 2015/02/07 %@ 978-3-939897-96-5 %G eng %U http://arxiv.org/abs/1502.02174 %R 10.4230/LIPIcs.TQC.2015.1 %0 Journal Article %J Physical Review Letters %D 2015 %T Parafermionic zero modes in ultracold bosonic systems %A Mohammad F. Maghrebi %A Sriram Ganeshan %A David J. Clarke %A Alexey V. Gorshkov %A Jay D. Sau %X Exotic topologically protected zero modes with parafermionic statistics (also called fractionalized Majorana modes) have been proposed to emerge in devices fabricated from a fractional quantum Hall system and a superconductor. The fractionalized statistics of these modes takes them an important step beyond the simplest non-Abelian anyons, Majorana fermions. Building on recent advances towards the realization of fractional quantum Hall states of bosonic ultracold atoms, we propose a realization of parafermions in a system consisting of Bose-Einstein-condensate trenches within a bosonic fractional quantum Hall state. We show that parafermionic zero modes emerge at the endpoints of the trenches and give rise to a topologically protected degeneracy. We also discuss methods for preparing and detecting these modes. %B Physical Review Letters %V 115 %P 065301 %8 2015/08/06 %G eng %U http://arxiv.org/abs/1504.04012v2 %N 6 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.115.065301 %0 Journal Article %J SampTA %D 2015 %T Phase Retrieval Without Small-Ball Probability Assumptions: Stability and Uniqueness %A Felix Krahmer %A Yi-Kai Liu %X We study stability and uniqueness for the phase retrieval problem. That is, we ask when is a signal x ∈ R n stably and uniquely determined (up to small perturbations), when one performs phaseless measurements of the form yi = |a T i x| 2 (for i = 1, . . . , N), where the vectors ai ∈ R n are chosen independently at random, with each coordinate aij ∈ R being chosen independently from a fixed sub-Gaussian distribution D. It is well known that for many common choices of D, certain ambiguities can arise that prevent x from being uniquely determined. In this note we show that for any sub-Gaussian distribution D, with no additional assumptions, most vectors x cannot lead to such ambiguities. More precisely, we show stability and uniqueness for all sets of vectors T ⊂ R n which are not too peaky, in the sense that at most a constant fraction of their mass is concentrated on any one coordinate. The number of measurements needed to recover x ∈ T depends on the complexity of T in a natural way, extending previous results of Eldar and Mendelson [12]. %B SampTA %P 411-414 %8 2015/05/25 %G eng %U http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7148923&tag=1 %0 Journal Article %J Physical Review Letters %D 2015 %T Phonon-Assisted Gain in a Semiconductor Double Quantum Dot Maser %A Michael Gullans %A Y. -Y. Liu %A J. Stehlik %A J. R. Petta %A J. M. Taylor %X We develop a microscopic model for the recently demonstrated double quantum dot (DQD) maser. In characterizing the gain of this device we find that, in addition to the direct stimulated emission of photons, there is a large contribution from the simultaneous emission of a photon and a phonon, i.e., the phonon sideband. We show that this phonon-assisted gain typically dominates the overall gain which leads to masing. Recent experimental data are well fit with our model. %B Physical Review Letters %V 114 %P 196802 %8 2015/05/13 %G eng %U http://arxiv.org/abs/1501.03499v3 %N 19 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.114.196802 %0 Journal Article %D 2015 %T The Power of Quantum Fourier Sampling %A Bill Fefferman %A Chris Umans %X A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer, unless the PH collapses. Aaronson and Arkhipov take this further by considering a distribution that can be sampled efficiently by linear optical quantum computation, that under two feasible conjectures, cannot even be approximately sampled classically within bounded total variation distance, unless the PH collapses. In this work we use Quantum Fourier Sampling to construct a class of distributions that can be sampled by a quantum computer. We then argue that these distributions cannot be approximately sampled classically, unless the PH collapses, under variants of the Aaronson and Arkhipov conjectures. In particular, we show a general class of quantumly sampleable distributions each of which is based on an "Efficiently Specifiable" polynomial, for which a classical approximate sampler implies an average-case approximation. This class of polynomials contains the Permanent but also includes, for example, the Hamiltonian Cycle polynomial, and many other familiar #P-hard polynomials. Although our construction, unlike that proposed by Aaronson and Arkhipov, likely requires a universal quantum computer, we are able to use this additional power to weaken the conjectures needed to prove approximate sampling hardness results. %8 2015/07/20 %G eng %U http://arxiv.org/abs/1507.05592v1 %0 Journal Article %J Communications of the ACM %D 2015 %T Programming the Quantum Future %A D. Scott Alexander %A Neil J. Ross %A Peter Selinger %A Jonathan M. Smith %A Benoît Valiron %X The earliest computers, like the ENIAC, were rare and heroically difficult to program. That difficulty stemmed from the requirement that algorithms be expressed in a "vocabulary" suited to the particular hardware available, ranging from function tables for the ENIAC to more conventional arithmetic and movement operations on later machines. Introduction of symbolic programming languages, exemplified by FORTRAN, solved a major difficulty for the next generation of computing devices by enabling specification of an algorithm in a form more suitable for human understanding, then translating this specification to a form executable by the machine. The "programming language" used for such specification bridged a semantic gap between the human and the computing device. It provided two important features: high-level abstractions, taking care of automated bookkeeping, and modularity, making it easier to reason about sub-parts of programs. %B Communications of the ACM %V 58 %P 52-61 %8 2015/08/01 %G eng %U http://cacm.acm.org/magazines/2015/8/189851-programming-the-quantum-future/fulltext#comments %N 8 %R 10.1145/2699415 %0 Journal Article %D 2015 %T Quantum Compressed Sensing Using 2-Designs %A Shelby Kimmel %A Yi-Kai Liu %X We develop a method for quantum process tomography that combines the efficiency of compressed sensing with the robustness of randomized benchmarking. Our method is robust to state preparation and measurement errors, and it achieves a quadratic speedup over conventional tomography when the unknown process is a generic unitary evolution. Our method is based on PhaseLift, a convex programming technique for phase retrieval. We show that this method achieves approximate recovery of almost all signals, using measurements sampled from spherical or unitary 2-designs. This is the first positive result on PhaseLift using 2-designs. We also show that exact recovery of all signals is possible using unitary 4-designs. Previous positive results for PhaseLift required spherical 4-designs, while PhaseLift was known to fail in certain cases when using spherical 2-designs. %8 2015/10/29 %G eng %U http://arxiv.org/abs/1510.08887 %0 Journal Article %J The Stanford Encyclopedia of Philosophy %D 2015 %T Quantum Entanglement and Information %A Jeffrey Bub %A Edward N. Zalta %X Quantum entanglement is a physical resource, like energy, associated with the peculiar nonclassical correlations that are possible between separated quantum systems. Entanglement can be measured, transformed, and purified. A pair of quantum systems in an entangled state can be used as a quantum information channel to perform computational and cryptographic tasks that are impossible for classical systems. The general study of the information-processing capabilities of quantum systems is the subject of quantum information theory. %B The Stanford Encyclopedia of Philosophy %8 02/07/2015 %G eng %U http://plato.stanford.edu/archives/sum2015/entries/qt-entangle/ %0 Journal Article %J Nature Photonics %D 2015 %T Quantum many-body models with cold atoms coupled to photonic crystals %A Douglas, J. S. %A Habibian, H. %A Hung, C.-L. %A Alexey V. Gorshkov %A Kimble, H. J. %A Chang, D. E. %B Nature Photonics %V 9 %P 326 - 331 %8 2015/04/04 %G eng %U http://www.nature.com/doifinder/10.1038/nphoton.2015.57 %N 5 %! Nature Photon %R 10.1038/nphoton.2015.57 %0 Journal Article %J Physical Review A %D 2015 %T Quantum Nonlinear Optics Near Optomechanical Instabilities %A Xunnong Xu %A Michael Gullans %A J. M. Taylor %X Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation pressure interaction. Here we show that it is not necessary to reach the single-photon strong-coupling regime in order to realize significant optomechanical nonlinearities. Instead, nonlinearities at the few quanta level can be achieved, even with weak-coupling, in a two-mode optomechanical system driven near instability. In this limit, we establish a new figure of merit for realizing strong nonlinearity which scales with the single-photon optomechanical coupling and the sideband resolution of the mechanical mode with respect to the cavity linewidth. We find that current devices based on optomechanical crystals, thought to be in the weak-coupling regime, can still achieve strong quantum nonlinearity; enabling deterministic interactions between single photons. %B Physical Review A %V 91 %P 013818 %8 2015/01/09 %G eng %U http://arxiv.org/abs/1404.3726v2 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.91.013818 %0 Journal Article %D 2015 %T Quantum vs Classical Proofs and Subset Verification %A Bill Fefferman %A Shelby Kimmel %X We study the ability of efficient quantum verifiers to decide properties of exponentially large subsets given either a classical or quantum witness. We develop a general framework that can be used to prove that QCMA machines, with only classical witnesses, cannot verify certain properties of subsets given implicitly via an oracle. We use this framework to prove an oracle separation between QCMA and QMA using an ``in-place'' permutation oracle, making the first progress on this question since Aaronson and Kuperberg in 2007. We also use the framework to prove a particularly simple standard oracle separation between QCMA and AM. %8 2015/10/22 %G eng %U http://arxiv.org/abs/1510.06750 %0 Journal Article %J Physical Review A %D 2015 %T Robust Single-Qubit Process Calibration via Robust Phase Estimation %A Shelby Kimmel %A Guang Hao Low %A Theodore J. Yoder %X An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the error in gates and then using controls to correct the implementation. Quantum process tomography is a standard technique for estimating these errors, but is both time consuming, (when one only wants to learn a few key parameters), and requires resources, like perfect state preparation and measurement, that might not be available. With the goal of efficiently estimating specific errors using minimal resources, we develop a parameter estimation technique, which can gauge two key parameters (amplitude and off-resonance errors) in a single-qubit gate with provable robustness and efficiency. In particular, our estimates achieve the optimal efficiency, Heisenberg scaling. Our main theorem making this possible is a robust version of the phase estimation procedure of Higgins et al. [B. L. Higgins, New J. Phys. 11, 073023 (2009)]. %B Physical Review A %V 92 %P 062315 %8 2015/12/08 %G eng %U http://arxiv.org/abs/1502.02677 %N 6 %R 10.1103/PhysRevA.92.062315 %0 Journal Article %J Physical Review A %D 2015 %T Self-heterodyne detection of the \it in-situ phase of an atomic-SQUID %A Ranchu Mathew %A Avinash Kumar %A Stephen Eckel %A Fred Jendrzejewski %A Gretchen K. Campbell %A Mark Edwards %A Eite Tiesinga %X We present theoretical and experimental analysis of an interferometric measurement of the {\it in-situ} phase drop across and current flow through a rotating barrier in a toroidal Bose-Einstein condensate (BEC). This experiment is the atomic analog of the rf-superconducting quantum interference device (SQUID). The phase drop is extracted from a spiral-shaped density profile created by the spatial interference of the expanding toroidal BEC and a reference BEC after release from all trapping potentials. We characterize the interferometer when it contains a single particle, which is initially in a coherent superposition of a torus and reference state, as well as when it contains a many-body state in the mean-field approximation. The single-particle picture is sufficient to explain the origin of the spirals, to relate the phase-drop across the barrier to the geometry of a spiral, and to bound the expansion times for which the {\it in-situ} phase can be accurately determined. Mean-field estimates and numerical simulations show that the inter-atomic interactions shorten the expansion time scales compared to the single-particle case. Finally, we compare the mean-field simulations with our experimental data and confirm that the interferometer indeed accurately measures the {\it in-situ} phase drop. %B Physical Review A %V 92 %P 033602 %8 2015/09/03 %G eng %U http://arxiv.org/abs/1506.09149v2 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.92.033602 %0 Journal Article %J Science %D 2015 %T Semiconductor double quantum dot micromaser %A Y. -Y. Liu %A J. Stehlik %A C. Eichler %A Michael Gullans %A J. M. Taylor %A J. R. Petta %X The coherent generation of light, from masers to lasers, relies upon the specific structure of the individual emitters that lead to gain. Devices operating as lasers in the few-emitter limit provide opportunities for understanding quantum coherent phenomena, from THz sources to quantum communication. Here we demonstrate a maser that is driven by single electron tunneling events. Semiconductor double quantum dots (DQDs) serve as a gain medium and are placed inside of a high quality factor microwave cavity. We verify maser action by comparing the statistics of the emitted microwave field above and below the maser threshold. %B Science %V 347 %P 285 - 287 %8 2015/01/15 %G eng %U http://arxiv.org/abs/1507.06359v1 %N 6219 %! Science %R 10.1126/science.aaa2501 %0 Journal Article %J Physical Review Letters %D 2015 %T Simulating Hamiltonian dynamics with a truncated Taylor series %A Dominic W. Berry %A Andrew M. Childs %A Richard Cleve %A Robin Kothari %A Rolando D. Somma %X We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations to directly apply the truncated Taylor series. %B Physical Review Letters %V 114 %P 090502 %8 2015/03/03 %G eng %U http://arxiv.org/abs/1412.4687v1 %N 9 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.114.090502 %0 Journal Article %J Quantum Information & Computation %D 2015 %T Tensor network non-zero testing %A Sevag Gharibian %A Zeph Landau %A Seung Woo Shin %A Guoming Wang %X Tensor networks are a central tool in condensed matter physics. In this paper, we initiate the study of tensor network non-zero testing (TNZ): Given a tensor network T, does T represent a non-zero vector? We show that TNZ is not in the Polynomial-Time Hierarchy unless the hierarchy collapses. We next show (among other results) that the special cases of TNZ on non-negative and injective tensor networks are in NP. Using this, we make a simple observation: The commuting variant of the MA-complete stoquastic k-SAT problem on D-dimensional qudits is in NP for logarithmic k and constant D. This reveals the first class of quantum Hamiltonians whose commuting variant is known to be in NP for all (1) logarithmic k, (2) constant D, and (3) for arbitrary interaction graphs. %B Quantum Information & Computation %V 15 %P 885-899 %8 2015/07/01 %G eng %U http://arxiv.org/abs/1406.5279 %N 9-10 %0 Journal Article %J Physical Review Letters %D 2015 %T Tunable Spin Qubit Coupling Mediated by a Multi-Electron Quantum Dot %A V. Srinivasa %A H. Xu %A J. M. Taylor %X We present an approach for entangling electron spin qubits localized on spatially separated impurity atoms or quantum dots via a multi-electron, two-level quantum dot. The effective exchange interaction mediated by the dot can be understood as the simplest manifestation of Ruderman-Kittel-Kasuya-Yosida exchange, and can be manipulated through gate voltage control of level splittings and tunneling amplitudes within the system. This provides both a high degree of tuneability and a means for realizing high-fidelity two-qubit gates between spatially separated spins, yielding an experimentally accessible method of coupling donor electron spins in silicon via a hybrid impurity-dot system. %B Physical Review Letters %V 114 %P 226803 %8 2015/06/04 %G eng %U http://arxiv.org/abs/1312.1711v3 %N 22 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.114.226803 %0 Journal Article %J Communications in Mathematical Physics %D 2015 %T Universal Subspaces for Local Unitary Groups of Fermionic Systems %A Lin Chen %A Jianxin Chen %A Dragomir Z. Djokovic %A Bei Zeng %X Let $\mathcal{V}=\wedge^N V$ be the $N$-fermion Hilbert space with $M$-dimensional single particle space $V$ and $2N\le M$. We refer to the unitary group $G$ of $V$ as the local unitary (LU) group. We fix an orthonormal (o.n.) basis $\ket{v_1},...,\ket{v_M}$ of $V$. Then the Slater determinants $e_{i_1,...,i_N}:= \ket{v_{i_1}\we v_{i_2}\we...\we v_{i_N}}$ with $i_1<...An obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical progress has mainly been limited to no-go results. Recent works have proposed the first efficient obfuscation algorithms for classical logic circuits, based on a notion of indistinguishability against polynomial-time adversaries. In this work, we propose a new notion of obfuscation, which we call partial-indistinguishability. This notion is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions. We describe universal gate sets for both classical and quantum computation, in which our definition of obfuscation can be met by polynomial-time algorithms. We also discuss some potential applications to testing quantum computers. We stress that the cryptographic security of these obfuscators, especially when composed with translation from other gate sets, remains an open question.

%B In Proceedings of the Sixth Conference on Theory of Quantum Computation, Communication and Cryptography (TQC14) %8 2014/08/21 %G eng %U http://arxiv.org/abs/1212.6358 %0 Journal Article %J Physical Review Letters %D 2014 %T Persistence of locality in systems with power-law interactions %A Zhe-Xuan Gong %A Michael Foss-Feig %A Spyridon Michalakis %A Alexey V. Gorshkov %X Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\alpha}$ interactions with $\alpha>D$. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not only bound but, except at long times, \emph{qualitatively reproduce} the short- and long-distance dynamical behavior following a local quench in an $XY$ chain and a transverse-field Ising chain. In addition to describing dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verified in a variety of ultracold-atomic and solid-state systems. %B Physical Review Letters %V 113 %8 2014/7/16 %G eng %U http://arxiv.org/abs/1401.6174v2 %N 3 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.113.030602 %0 Journal Article %J Eurocrypt %D 2014 %T Privacy Amplification in the Isolated Qubits Model %A Yi-Kai Liu %X Isolated qubits are a special class of quantum devices, which can be used to implement tamper-resistant cryptographic hardware such as one-time memories (OTM's). Unfortunately, these OTM constructions leak some information, and standard methods for privacy amplification cannot be applied here, because the adversary has advance knowledge of the hash function that the honest parties will use. In this paper we show a stronger form of privacy amplification that solves this problem, using a fixed hash function that is secure against all possible adversaries in the isolated qubits model. This allows us to construct single-bit OTM's which only leak an exponentially small amount of information. We then study a natural generalization of the isolated qubits model, where the adversary is allowed to perform a polynomially-bounded number of entangling gates, in addition to unbounded local operations and classical communication (LOCC). We show that our technique for privacy amplification is also secure in this setting. %B Eurocrypt %P 785-814 %8 2014/10/15 %G eng %U http://arxiv.org/abs/1410.3918v2 %! EUROCRYPT 2015 %R 10.1007/978-3-662-46803-6_26 %0 Journal Article %J Ann. Phys. %D 2014 %T Probing many-body interactions in an optical lattice clock %A Rey, A M %A Alexey V. Gorshkov %A Kraus, C V %A Martin, M J %A Bishof, M %A Swallows, M D %A Zhang, X %A Benko, C %A Ye, J %A Lemke, N D %A Ludlow, A D %B Ann. Phys. %V 340 %P 311 %G eng %U http://www.sciencedirect.com/science/article/pii/S0003491613002546 %0 Journal Article %D 2014 %T Quantum Algorithms for Curve Fitting %A Guoming Wang %X We present quantum algorithms for estimating the best-fit parameters and the quality of least-square curve fitting. The running times of these algorithms are polynomial in logn, d, κ, ν, χ, 1/Φ and 1/ϵ, where n is the number of data points to be fitted, d is the dimension of feature vectors, κ is the condition number of the design matrix, ν and χ are some parameters reflecting the variances of the design matrix and response vector, Φ is the fit quality, and ϵ is the tolerable error. Different from previous quantum algorithms for these tasks, our algorithms do not require the design matrix to be sparse, and they do completely determine the fitted curve. They are developed by combining phase estimation and the density matrix exponentiation technique for dense Hamiltonian simulation. %8 2014/04/02 %G eng %U http://arxiv.org/abs/1402.0660 %0 Journal Article %D 2014 %T Quantum Algorithms for Fermionic Quantum Field Theories %A Stephen P. Jordan %A Keith S. M. Lee %A John Preskill %X Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu model, a theory in two spacetime dimensions with quartic interactions. The algorithm introduces new techniques to meet the additional challenges posed by the characteristics of fermionic fields, and its run time is polynomial in the desired precision and the energy. Thus, it constitutes further progress towards an efficient quantum algorithm for simulating the Standard Model of particle physics. %8 2014/04/28 %G eng %U http://arxiv.org/abs/1404.7115v1 %0 Journal Article %J Journal of Mathematical Cryptology %D 2014 %T Quantum computation of discrete logarithms in semigroups %A Andrew M. Childs %A Gábor Ivanyos %X We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete logarithms in semigroups are insecure against quantum attacks. In contrast, we show that some generalizations of the discrete log problem are hard in semigroups despite being easy in groups. We relate a shifted version of the discrete log problem in semigroups to the dihedral hidden subgroup problem, and we show that the constructive membership problem with respect to $k \ge 2$ generators in a black-box abelian semigroup of order $N$ requires $\tilde \Theta(N^{\frac{1}{2}-\frac{1}{2k}})$ quantum queries. %B Journal of Mathematical Cryptology %V 8 %8 2014/01/1 %G eng %U http://arxiv.org/abs/1310.6238v2 %N 4 %! Journal of Mathematical Cryptology 8 %R 10.1515/jmc-2013-0038 %0 Journal Article %J Quantum Information and Computation %D 2014 %T Quantum Computation of Scattering in Scalar Quantum Field Theories %A Stephen P. Jordan %A Keith S. M. Lee %A John Preskill %X Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally, and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive phi-fourth theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling. %B Quantum Information and Computation %V 14 %P 1014-1080 %8 2014/09/01 %G eng %U http://arxiv.org/abs/1112.4833v1 %N 11-12 %! Quantum Information and Computation 14 %0 Journal Article %J Physical Review A %D 2014 %T Quantum correlations and entanglement in far-from-equilibrium spin systems %A Kaden R. A. Hazzard %A Mauritz van den Worm %A Michael Foss-Feig %A Salvatore R. Manmana %A Emanuele Dalla Torre %A Tilman Pfau %A Michael Kastner %A Ana Maria Rey %X By applying complementary analytic and numerical methods, we investigate the dynamics of spin-$1/2$ XXZ models with variable-range interactions in arbitrary dimensions. The dynamics we consider is initiated from uncorrelated states that are easily prepared in experiments, and can be equivalently viewed as either Ramsey spectroscopy or a quantum quench. Our primary focus is the dynamical emergence of correlations and entanglement in these far-from-equilibrium interacting quantum systems: we characterize these correlations by the entanglement entropy, concurrence, and squeezing, which are inequivalent measures of entanglement corresponding to different quantum resources. In one spatial dimension, we show that the time evolution of correlation functions manifests a non-perturbative dynamic singularity. This singularity is characterized by a universal power-law exponent that is insensitive to small perturbations. Explicit realizations of these models in current experiments using polar molecules, trapped ions, Rydberg atoms, magnetic atoms, and alkaline-earth and alkali atoms in optical lattices, along with the relative merits and limitations of these different systems, are discussed. %B Physical Review A %V 90 %8 2014/12/15 %G eng %U http://arxiv.org/abs/1406.0937v1 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.90.063622 %0 Journal Article %J International Journal of Theoretical Physics %D 2014 %T Quantum Correlations and the Measurement Problem %A Jeffrey Bub %X The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope of local correlations. Such correlations cannot be simulated with classical resources, which generate classical correlations represented by the points in a simplex, where the vertices of the simplex represent joint deterministic states that are the common causes of the correlations. The `no go' hidden variable theorems tell us that we can't shoe-horn correlations outside the local polytope into a classical simplex by supposing that something has been left out of the story. The replacement of the classical simplex by the quantum convex set as the structure representing probabilistic correlations is the analogue for quantum mechanics of the replacement of Newton's Euclidean space and time by Minkowski spacetime in special relativity. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are generic features of correlations that lie outside the local correlation polytope. This paper is an elaboration of these ideas, and its consequences for the measurement problem of quantum mechanics. A large part of the difficulty is removed by seeing that the inconsistency in reconciling the entangled state at the end of a quantum measurement process with the definiteness of the macroscopic pointer reading and the definiteness of the correlated value of the measured micro-observable is only apparent and depends on a stipulation that is not required by the structure of the quantum possibility space. Replacing this stipulation by an alternative consistent stipulation resolves the problem. %B International Journal of Theoretical Physics %V 53 %P 3346 - 3369 %8 2013/6/30 %G eng %U http://arxiv.org/abs/1210.6371v3 %N 10 %! Int J Theor Phys %R 10.1007/s10773-013-1695-z %0 Journal Article %J Physical Review A %D 2014 %T Quantum Interactions with Closed Timelike Curves and Superluminal Signaling %A Jeffrey Bub %A Allen Stairs %X There is now a significant body of results on quantum interactions with closed timelike curves (CTCs) in the quantum information literature, for both the Deutsch model of CTC interactions (D-CTCs) and the projective model (P-CTCs). As a consequence, there is a prima facie argument exploiting entanglement that CTC interactions would enable superluminal and, indeed, effectively instantaneous signaling. In cases of spacelike separation between the sender of a signal and the receiver, whether a receiver measures the local part of an entangled state or a disentangled state to access the signal can depend on the reference frame. We propose a consistency condition that gives priority to either an entangled perspective or a disentangled perspective in spacelike separated scenarios. For D-CTC interactions, the consistency condition gives priority to frames of reference in which the state is disentangled, while for P-CTC interactions the condition selects the entangled state. Using the consistency condition, we show that there is a procedure that allows Alice to signal to Bob in the past via relayed superluminal communications between spacelike separated Alice and Clio, and spacelike separated Clio and Bob. This opens the door to time travel paradoxes in the classical domain. Ralph (arXiv:1107.4675) first pointed this out for P-CTCs, but we show that Ralph's procedure for a 'radio to the past' is flawed. Since both D-CTCs and P-CTCs allow classical information to be sent around a spacetime loop, it follows from a result by Aaronson and Watrous (Proc.Roy.Soc.A, 465:631-647 (2009)) for CTC-enhanced classical computation that a quantum computer with access to P-CTCs would have the power of PSPACE, equivalent to a D-CTC-enhanced quantum computer. %B Physical Review A %V 89 %8 2014/2/12 %G eng %U http://arxiv.org/abs/1309.4751v4 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.89.022311 %0 Journal Article %D 2014 %T A Quantum Network of Silicon Qubits using Mid-Infrared Graphene Plasmons %A Michael Gullans %A J. M. Taylor %X We consider a quantum network of mid-infrared, graphene plasmons coupled to the hydrogen-like excited states of group-V donors in silicon. First, we show how to use plasmon-enhanced light-matter interactions to achieve single-shot spin readout of the donor qubits via optical excitation and electrical detection of the emitted plasmons. We then show how plasmons in high mobility graphene nanoribbons can be used to achieve high-fidelity, two-qubit gates and entanglement of distant Si donor qubits. The proposed device is readily compatible with existing technology and fabrication methods. %8 2014/07/25 %G eng %U http://arxiv.org/abs/1407.7035v1 %0 Journal Article %D 2014 %T Quipper: Concrete Resource Estimation in Quantum Algorithms %A Jonathan M. Smith %A Neil J. Ross %A Peter Selinger %A Benoît Valiron %XDespite the rich literature on quantum algorithms, there is a surprisingly small amount of coverage of their concrete logical design and implementation. Most resource estimation is done at the level of complexity analysis, but actual concrete numbers (of quantum gates, qubits, etc.) can differ by orders of magnitude. The line of work we present here is a formal framework to write, and reason about, quantum algorithms. Specifically, we designed a language, Quipper, with scalability in mind, and we are able to report actual resource counts for seven non-trivial algorithms found in the quantum computer science literature.

%8 2014/12/01 %G eng %U http://arxiv.org/abs/1412.0625v1 %0 Journal Article %J Physical Review A %D 2014 %T Remote tomography and entanglement swapping via von Neumann–Arthurs–Kelly interaction %A S. M. Roy %A Abhinav Deshpande %A Nitica Sakharwade %X We propose an interaction-based method for remote tomography and entanglement swapping. Alice arranges a von Neumann-Arthurs-Kelly interaction between a system particle P and two apparatus particles A1,A2, and then transports the latter to Bob. Bob can reconstruct the unknown initial state of particle P not received by him by quadrature measurements on A1,A2. Further, if another particle P′ in Alice's hands is EPR entangled with P, it will be EPR entangled with the distant pair A1,A2. This method will be contrasted with the usual teleportation protocols. %B Physical Review A %V 89 %P 052107 %8 2014/05/09 %G eng %U http://journals.aps.org/pra/abstract/10.1103/PhysRevA.89.052107 %N 5 %R http://dx.doi.org/10.1103/PhysRevA.89.052107 %0 Journal Article %J Physical Review X %D 2014 %T Robust Extraction of Tomographic Information via Randomized Benchmarking %A Shelby Kimmel %A Marcus P. da Silva %A Colm A. Ryan %A Blake R. Johnson %A Thomas Ohki %X We describe how randomized benchmarking can be used to reconstruct the unital part of any trace-preserving quantum map, which in turn is sufficient for the full characterization of any unitary evolution, or more generally, any unital trace-preserving evolution. This approach inherits randomized benchmarking's robustness to preparation and measurement imperfections, therefore avoiding systematic errors caused by these imperfections. We also extend these techniques to efficiently estimate the average fidelity of a quantum map to unitary maps outside of the Clifford group. The unitaries we consider include operations commonly used to achieve universal quantum computation in a fault-tolerant setting. In addition, we rigorously bound the time and sampling complexities of randomized benchmarking procedures. %B Physical Review X %V 4 %8 2014/3/25 %G eng %U http://arxiv.org/abs/1306.2348v1 %N 1 %! Phys. Rev. X %R 10.1103/PhysRevX.4.011050 %0 Journal Article %J Physical Review A %D 2014 %T Scattering resonances and bound states for strongly interacting Rydberg polaritons %A P. Bienias %A S. Choi %A O. Firstenberg %A Mohammad F. Maghrebi %A Michael Gullans %A M. D. Lukin %A Alexey V. Gorshkov %A H. P. Büchler %X We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments. %B Physical Review A %V 90 %8 2014/11/3 %G eng %U http://arxiv.org/abs/1402.7333v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.90.053804 %0 Journal Article %J CRYPTO %D 2014 %T Single-shot security for one-time memories in the isolated qubits model %A Yi-Kai Liu %X One-time memories (OTM's) are simple, tamper-resistant cryptographic devices, which can be used to implement sophisticated functionalities such as one-time programs. Can one construct OTM's whose security follows from some physical principle? This is not possible in a fully-classical world, or in a fully-quantum world, but there is evidence that OTM's can be built using "isolated qubits" -- qubits that cannot be entangled, but can be accessed using adaptive sequences of single-qubit measurements. Here we present new constructions for OTM's using isolated qubits, which improve on previous work in several respects: they achieve a stronger "single-shot" security guarantee, which is stated in terms of the (smoothed) min-entropy; they are proven secure against adversaries who can perform arbitrary local operations and classical communication (LOCC); and they are efficiently implementable. These results use Wiesner's idea of conjugate coding, combined with error-correcting codes that approach the capacity of the q-ary symmetric channel, and a high-order entropic uncertainty relation, which was originally developed for cryptography in the bounded quantum storage model. %B CRYPTO %V Part II %P 19-36 %8 2014/02/01 %G eng %U http://arxiv.org/abs/1402.0049v2 %! CRYPTO 2014 %R 10.1007/978-3-662-44381-1_2 %0 Journal Article %J Physical Review A %D 2014 %T Spatial search by continuous-time quantum walks on crystal lattices %A Andrew M. Childs %A Yimin Ge %X We consider the problem of searching a general $d$-dimensional lattice of $N$ vertices for a single marked item using a continuous-time quantum walk. We demand locality, but allow the walk to vary periodically on a small scale. By constructing lattice Hamiltonians exhibiting Dirac points in their dispersion relations and exploiting the linear behaviour near a Dirac point, we develop algorithms that solve the problem in a time of $O(\sqrt N)$ for $d>2$ and $O(\sqrt N \log N)$ in $d=2$. In particular, we show that such algorithms exist even for hypercubic lattices in any dimension. Unlike previous continuous-time quantum walk algorithms on hypercubic lattices in low dimensions, our approach does not use external memory. %B Physical Review A %V 89 %8 2014/5/30 %G eng %U http://arxiv.org/abs/1403.2676v2 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.89.052337 %0 Journal Article %J Physical Review A %D 2014 %T Spin-orbit-coupled topological Fulde-Ferrell states of fermions in a harmonic trap %A Lei Jiang %A Eite Tiesinga %A Xia-Ji Liu %A Hui Hu %A Han Pu %X Motivated by recent experimental breakthroughs in generating spin-orbit coupling in ultracold Fermi gases using Raman laser beams, we present a systematic study of spin-orbit-coupled Fermi gases confined in a quasi-one-dimensional trap in the presence of an in-plane Zeeman field (which can be realized using a finite two-photon Raman detuning). We find that a topological Fulde-Ferrell state will emerge, featuring finite-momentum Cooper pairing and zero-energy Majorana excitations localized near the edge of the trap based on the self-consistent Bogoliubov-de Genes (BdG) equations. We find analytically the wavefunctions of the Majorana modes. Finally using the time-dependent BdG we show how the finite-momentum pairing field manifests itself in the expansion dynamics of the atomic cloud. %B Physical Review A %V 90 %8 2014/11/7 %G eng %U http://arxiv.org/abs/1404.6211v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.90.053606 %0 Journal Article %J Quantum Information Computation %D 2014 %T Strong Equivalence of Reversible Circuits is coNP-complete %A Stephen P. Jordan %K complexity %K reversible circuits %XIt is well-known that deciding equivalence of logic circuits is a coNP-complete problem. As a corollary, the problem of deciding weak equivalence of reversible circuits, i.e. allowing initialized ancilla bits in the input and ignoring "garbage" ancilla bits in the output, is also coNP-complete. The complexity of deciding strong equivalence, including the ancilla bits, is less obvious and may depend on gate set. Here we use Barrington's theorem to show that deciding strong equivalence of reversible circuits built from the Fredkin gate is coNP-complete. This implies coNP-completeness of deciding strong equivalence for other commonly used universal reversible gate sets, including any gate set that includes the Toffoli or Fredkin gate.

%B Quantum Information Computation %V 14 %P 1302–1307 %8 2014/11/01 %G eng %U http://dl.acm.org/citation.cfm?id=2685179.2685182 %0 Journal Article %J Physical Review Letters %D 2014 %T Suppressing the loss of ultracold molecules via the continuous quantum Zeno effect %A Bihui Zhu %A Bryce Gadway %A Michael Foss-Feig %A Johannes Schachenmayer %A Michael Wall %A Kaden R. A. Hazzard %A Bo Yan %A Steven A. Moses %A Jacob P. Covey %A Deborah S. Jin %A Jun Ye %A Murray Holland %A Ana Maria Rey %X We investigate theoretically the suppression of two-body losses when the on-site loss rate is larger than all other energy scales in a lattice. This work quantitatively explains the recently observed suppression of chemical reactions between two rotational states of fermionic KRb molecules confined in one-dimensional tubes with a weak lattice along the tubes [Yan et al., Nature 501, 521-525 (2013)]. New loss rate measurements performed for different lattice parameters but under controlled initial conditions allow us to show that the loss suppression is a consequence of the combined effects of lattice confinement and the continuous quantum Zeno effect. A key finding, relevant for generic strongly reactive systems, is that while a single-band theory can qualitatively describe the data, a quantitative analysis must include multiband effects. Accounting for these effects reduces the inferred molecule filling fraction by a factor of five. A rate equation can describe much of the data, but to properly reproduce the loss dynamics with a fixed filling fraction for all lattice parameters we develop a mean-field model and benchmark it with numerically exact time-dependent density matrix renormalization group calculations. %B Physical Review Letters %V 112 %8 2014/2/20 %G eng %U http://arxiv.org/abs/1310.2221v2 %N 7 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.112.070404 %0 Journal Article %J Physical Review A %D 2014 %T Symmetric Extension of Two-Qubit States %A Jianxin Chen %A Zhengfeng Ji %A David Kribs %A Norbert Lütkenhaus %A Bei Zeng %X Quantum key distribution uses public discussion protocols to establish shared secret keys. In the exploration of ultimate limits to such protocols, the property of symmetric extendibility of underlying bipartite states $\rho_{AB}$ plays an important role. A bipartite state $\rho_{AB}$ is symmetric extendible if there exits a tripartite state $\rho_{ABB'}$, such that the $AB$ marginal state is identical to the $AB'$ marginal state, i.e. $\rho_{AB'}=\rho_{AB}$. For a symmetric extendible state $\rho_{AB}$, the first task of the public discussion protocol is to break this symmetric extendibility. Therefore to characterize all bi-partite quantum states that possess symmetric extensions is of vital importance. We prove a simple analytical formula that a two-qubit state $\rho_{AB}$ admits a symmetric extension if and only if $\tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}$. Given the intimate relationship between the symmetric extension problem and the quantum marginal problem, our result also provides the first analytical necessary and sufficient condition for the quantum marginal problem with overlapping marginals. %B Physical Review A %V 90 %8 2014/9/17 %G eng %U http://arxiv.org/abs/1310.3530v2 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.90.032318 %0 Journal Article %J Journal of Mathematical Physics %D 2014 %T Unextendible Product Basis for Fermionic Systems %A Jianxin Chen %A Lin Chen %A Bei Zeng %X We discuss the concept of unextendible product basis (UPB) and generalized UPB for fermionic systems, using Slater determinants as an analogue of product states, in the antisymmetric subspace $\wedge^ N \bC^M$. We construct an explicit example of generalized fermionic unextendible product basis (FUPB) of minimum cardinality $N(M-N)+1$ for any $N\ge2,M\ge4$. We also show that any bipartite antisymmetric space $\wedge^ 2 \bC^M$ of codimension two is spanned by Slater determinants, and the spaces of higher codimension may not be spanned by Slater determinants. Furthermore, we construct an example of complex FUPB of $N=2,M=4$ with minimum cardinality $5$. In contrast, we show that a real FUPB does not exist for $N=2,M=4$ . Finally we provide a systematic construction for FUPBs of higher dimensions using FUPBs and UPBs of lower dimensions. %B Journal of Mathematical Physics %V 55 %P 082207 %8 2014/01/01 %G eng %U http://arxiv.org/abs/1312.4218v1 %N 8 %! J. Math. Phys. %R 10.1063/1.4893358 %0 Journal Article %J Science %D 2013 %T All-Optical Switch and Transistor Gated by One Stored Photon %A Wenlan Chen %A Kristin M. Beck %A Robert Bücker %A Michael Gullans %A Mikhail D. Lukin %A Haruka Tanji-Suzuki %A Vladan Vuletic %X The realization of an all-optical transistor where one 'gate' photon controls a 'source' light beam, is a long-standing goal in optics. By stopping a light pulse in an atomic ensemble contained inside an optical resonator, we realize a device in which one stored gate photon controls the resonator transmission of subsequently applied source photons. A weak gate pulse induces bimodal transmission distribution, corresponding to zero and one gate photons. One stored gate photon produces fivefold source attenuation, and can be retrieved from the atomic ensemble after switching more than one source photon. Without retrieval, one stored gate photon can switch several hundred source photons. With improved storage and retrieval efficiency, our work may enable various new applications, including photonic quantum gates, and deterministic multiphoton entanglement. %B Science %V 341 %P 768 - 770 %8 2013/07/04 %G eng %U http://arxiv.org/abs/1401.3194v1 %N 6147 %! Science %R 10.1126/science.1238169 %0 Journal Article %J Nature (London) %D 2013 %T Attractive Photons in a Quantum Nonlinear Medium %A Ofer Firstenberg %A Thibault Peyronel %A Qi-Yu Liang %A Alexey V. Gorshkov %A Mikhail D. Lukin %A Vladan Vuletic %B Nature (London) %V 502 %P 71 %G eng %U http://dx.doi.org/10.1038/nature12512 %0 Journal Article %J Innovations in Theoretical Computer Science (ITCS) %D 2013 %T Building one-time memories from isolated qubits %A Yi-Kai Liu %X One-time memories (OTM's) are simple tamper-resistant cryptographic devices, which can be used to implement one-time programs, a very general form of software protection and program obfuscation. Here we investigate the possibility of building OTM's using quantum mechanical devices. It is known that OTM's cannot exist in a fully-quantum world or in a fully-classical world. Instead, we propose a new model based on "isolated qubits" -- qubits that can only be accessed using local operations and classical communication (LOCC). This model combines a quantum resource (single-qubit measurements) with a classical restriction (on communication between qubits), and can be implemented using current technologies, such as nitrogen vacancy centers in diamond. In this model, we construct OTM's that are information-theoretically secure against one-pass LOCC adversaries that use 2-outcome measurements. Our construction resembles Wiesner's old idea of quantum conjugate coding, implemented using random error-correcting codes; our proof of security uses entropy chaining to bound the supremum of a suitable empirical process. In addition, we conjecture that our random codes can be replaced by some class of efficiently-decodable codes, to get computationally-efficient OTM's that are secure against computationally-bounded LOCC adversaries. In addition, we construct data-hiding states, which allow an LOCC sender to encode an (n-O(1))-bit messsage into n qubits, such that at most half of the message can be extracted by a one-pass LOCC receiver, but the whole message can be extracted by a general quantum receiver. %B Innovations in Theoretical Computer Science (ITCS) %P 269-286 %8 2013/04/18 %G eng %U http://arxiv.org/abs/1304.5007v2 %! Proceedings of the 5th conference on Innovations in Theoretical Computer Science (ITCS 2014) %R 10.1145/2554797.2554823 %0 Journal Article %J Physical Review B %D 2013 %T Controllable quantum spin glasses with magnetic impurities embedded in quantum solids %A Mikhail Lemeshko %A Norman Y. Yao %A Alexey V. Gorshkov %A Hendrik Weimer %A Steven D. Bennett %A Takamasa Momose %A Sarang Gopalakrishnan %X Magnetic impurities embedded in inert solids can exhibit long coherence times and interact with one another via their intrinsic anisotropic dipolar interaction. We argue that, as a consequence of these properties, disordered ensembles of magnetic impurities provide an effective platform for realizing a controllable, tunable version of the dipolar quantum spin glass seen in LiHo$_x$Y$_{1-x}$F$_4$. Specifically, we propose and analyze a system composed of dysprosium atoms embedded in solid helium. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases. %B Physical Review B %V 88 %8 2013/7/24 %G eng %U http://arxiv.org/abs/1307.1130v1 %N 1 %! Phys. Rev. B %R 10.1103/PhysRevB.88.014426 %0 Journal Article %J Physical Review A %D 2013 %T Controlling the group velocity of colliding atomic Bose-Einstein condensates with Feshbach resonances %A Ranchu Mathew %A Eite Tiesinga %X We report on a proposal to change the group velocity of a small Bose Einstein Condensate (BEC) upon collision with another BEC in analogy to slowing of light passing through dispersive media. We make use of ultracold collisions near a magnetic Feshbach resonance, which gives rise to a sharp variation in scattering length with collision energy and thereby changes the group velocity. A generalized Gross-Pitaveskii equation is derived for a small BEC moving through a larger stationary BEC. We denote the two condensates by laser and medium BEC, respectively, to highlight the analogy to a laser pulse travelling through a medium. We derive an expression for the group velocity in a homogeneous medium as well as for the difference in distance, $\delta$, covered by the laser BEC in the presence and absence of a finite-sized medium BEC with a Thomas-Fermi density distribution. For a medium and laser of the same isotopic species, the shift $\delta$ has an upper bound of twice the Thomas-Fermi radius of the medium. For typical narrow Feshbach resonances and a medium with number density $10^{15}$ cm$^{-3}$ up to 85% of the upper bound can be achieved, making the effect experimentally observable. We also derive constraints on the experimental realization of our proposal. %B Physical Review A %V 87 %8 2013/5/10 %G eng %U http://arxiv.org/abs/1301.4234v2 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.87.053608 %0 Journal Article %J Physical Review Letters %D 2013 %T Dissipative Many-body Quantum Optics in Rydberg Media %A Alexey V. Gorshkov %A Rejish Nath %A Thomas Pohl %X We develop a theoretical framework for the dissipative propagation of quantized light in interacting optical media under conditions of electromagnetically induced transparency (EIT). The theory allows us to determine the peculiar spatiotemporal structure of the output of two complementary Rydberg-EIT-based light-processing modules: the recently demonstrated single-photon filter and the recently proposed single-photon subtractor, which, respectively, let through and absorb a single photon. In addition to being crucial for applications of these and other optical quantum devices, the theory opens the door to the study of exotic dissipative many-body dynamics of strongly interacting photons in nonlinear nonlocal media. %B Physical Review Letters %V 110 %8 2013/4/9 %G eng %U http://arxiv.org/abs/1211.7060v1 %N 15 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.110.153601 %0 Journal Article %J New Journal of Physics %D 2013 %T Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence %A Michael Foss-Feig %A Kaden R A Hazzard %A John J Bollinger %A Ana Maria Rey %A Charles W Clark %X Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms realize long-ranged Ising models, which even in the absence of a transverse field can give rise to highly non-classical dynamics and long-range quantum correlations. In the first part of this paper, we present a detailed theoretical framework for studying the dynamics of such systems driven (at time t=0) into arbitrary unentangled non-equilibrium states, thus greatly extending and unifying the work of Ref. [1]. Specifically, we derive exact expressions for closed-time-path ordered correlation functions, and use these to study experimentally relevant observables, e.g. Bloch vector and spin-squeezing dynamics. In the second part, these correlation functions are then used to derive closed-form expressions for the dynamics of arbitrary spin-spin correlation functions in the presence of both T_1 (spontaneous spin relaxation/excitation) and T_2 (dephasing) type decoherence processes. Even though the decoherence is local, our solution reveals that the competition between Ising dynamics and T_1 decoherence gives rise to an emergent non-local dephasing effect, thereby drastically amplifying the degradation of quantum correlations. In addition to identifying the mechanism of this deleterious effect, our solution points toward a scheme to eliminate it via measurement-based coherent feedback. %B New Journal of Physics %V 15 %P 113008 %8 2013/11/07 %G eng %U http://arxiv.org/abs/1306.0172v1 %N 11 %! New J. Phys. %R 10.1088/1367-2630/15/11/113008 %0 Journal Article %J Proceedings of TQC 2013 %D 2013 %T Easy and hard functions for the Boolean hidden shift problem %A Andrew M. Childs %A Robin Kothari %A Maris Ozols %A Martin Roetteler %X We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends strongly on f. We demonstrate that the easiest instances of this problem correspond to bent functions, in the sense that an exact one-query algorithm exists if and only if the function is bent. We partially characterize the hardest instances, which include delta functions. Moreover, we show that the problem is easy for random functions, since two queries suffice. Our algorithm for random functions is based on performing the pretty good measurement on several copies of a certain state; its analysis relies on the Fourier transform. We also use this approach to improve the quantum rejection sampling approach to the Boolean hidden shift problem. %B Proceedings of TQC 2013 %V 22 %P 50-79 %8 2013/04/16 %G eng %U http://arxiv.org/abs/1304.4642v1 %! Proceedings of TQC 2013 %R 10.4230/LIPIcs.TQC.2013.50 %0 Journal Article %J Physical Review Letters %D 2013 %T Electrically-protected resonant exchange qubits in triple quantum dots %A J. M. Taylor %A V. Srinivasa %A J. Medford %X We present a modulated microwave approach for quantum computing with qubits comprising three spins in a triple quantum dot. This approach includes single- and two-qubit gates that are protected against low-frequency electrical noise, due to an operating point with a narrowband response to high frequency electric fields. Furthermore, existing double quantum dot advances, including robust preparation and measurement via spin-to-charge conversion, are immediately applicable to the new qubit. Finally, the electric dipole terms implicit in the high frequency coupling enable strong coupling with superconducting microwave resonators, leading to more robust two-qubit gates. %B Physical Review Letters %V 111 %8 2013/7/31 %G eng %U http://arxiv.org/abs/1304.3407v2 %N 5 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.111.050502 %0 Journal Article %J Foundations and Trends in Theoretical Computer Science %D 2013 %T Evasiveness of Graph Properties and Topological Fixed-Point Theorems %A Carl Miller %XMany graph properties (e.g., connectedness, containing a complete subgraph) are known to be difficult to check. In a decision-tree model, the cost of an algorithm is measured by the number of edges in the graph that it queries. R. Karp conjectured in the early 1970s that all monotone graph properties are evasive -- that is, any algorithm which computes a monotone graph property must check all edges in the worst case. This conjecture is unproven, but a lot of progress has been made. Starting with the work of Kahn, Saks, and Sturtevant in 1984, topological methods have been applied to prove partial results on the Karp conjecture. This text is a tutorial on these topological methods. I give a fully self-contained account of the central proofs from the paper of Kahn, Saks, and Sturtevant, with no prior knowledge of topology assumed. I also briefly survey some of the more recent results on evasiveness.

%B Foundations and Trends in Theoretical Computer Science %V 7 %P 337-415 %8 2013/05/16 %G eng %U http://dx.doi.org/10.1561/0400000055 %R 10.1561/0400000055 %0 Journal Article %J Physical Review A %D 2013 %T Experimental Performance of a Quantum Simulator: Optimizing Adiabatic Evolution and Identifying Many-Body Ground States %A Philip Richerme %A Crystal Senko %A Jacob Smith %A Aaron Lee %A Simcha Korenblit %A Christopher Monroe %X We use local adiabatic evolution to experimentally create and determine the ground state spin ordering of a fully-connected Ising model with up to 14 spins. Local adiabatic evolution -- in which the system evolution rate is a function of the instantaneous energy gap -- is found to maximize the ground state probability compared with other adiabatic methods while only requiring knowledge of the lowest $\sim N$ of the $2^N$ Hamiltonian eigenvalues. We also demonstrate that the ground state ordering can be experimentally identified as the most probable of all possible spin configurations, even when the evolution is highly non-adiabatic. %B Physical Review A %V 88 %8 2013/7/31 %G eng %U http://arxiv.org/abs/1305.2253v1 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.88.012334 %0 Journal Article %J Physical Review Letters %D 2013 %T Far from equilibrium quantum magnetism with ultracold polar molecules %A Kaden R. A. Hazzard %A Salvatore R. Manmana %A Michael Foss-Feig %A Ana Maria Rey %X Recent theory has indicated how to emulate tunable models of quantum magnetism with ultracold polar molecules. Here we show that present molecule optical lattice experiments can accomplish three crucial goals for quantum emulation, despite currently being well below unit filling and not quantum degenerate. The first is to verify and benchmark the models proposed to describe these systems. The second is to prepare correlated and possibly useful states in well-understood regimes. The third is to explore many-body physics inaccessible to existing theoretical techniques. Our proposal relies on a non-equilibrium protocol that can be viewed either as Ramsey spectroscopy or an interaction quench. It uses only routine experimental tools available in any ultracold molecule experiment. %B Physical Review Letters %V 110 %8 2013/2/11 %G eng %U http://arxiv.org/abs/1209.4076v1 %N 7 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.110.075301 %0 Journal Article %J Physical Review A %D 2013 %T Formation and decay of Bose-Einstein condensates in an excited band of a double-well optical lattice %A Saurabh Paul %A Eite Tiesinga %X We study the formation and collision-aided decay of an ultra-cold atomic Bose-Einstein condensate in the first excited band of a double-well 2D-optical lattice with weak harmonic confinement in the perpendicular $z$ direction. This lattice geometry is based on an experiment by Wirth et al. The double well is asymmetric, with the local ground state in the shallow well nearly degenerate with the first excited state of the adjacent deep well. We compare the band structure obtained from a tight-binding (TB) model with that obtained numerically using a plane wave basis. We find the TB model to be in quantitative agreement for the lowest two bands, qualitative for next two bands, and inadequate for even higher bands. The band widths of the excited bands are much larger than the harmonic oscillator energy spacing in the $z$ direction. We then study the thermodynamics of a non-interacting Bose gas in the first excited band. We estimate the condensate fraction and critical temperature, $T_c$, as functions of lattice parameters. For typical atom numbers, the critical energy $k_BT_c$, with $k_B$ the Boltzmann constant, is larger than the excited band widths and harmonic oscillator energy. Using conservation of total energy and atom number, we show that the temperature increases after the lattice transformation. Finally, we estimate the time scale for a two-body collision-aided decay of the condensate as a function of lattice parameters. The decay involves two processes, the dominant one in which both colliding atoms decay to the ground band, and the second involving excitation of one atom to a higher band. For this estimate, we have used TB wave functions for the lowest four bands, and numerical estimates for higher bands. The decay rate rapidly increases with lattice depth, but stays smaller than the tunneling rate between the $s$ and $p$ orbitals in adjacent wells. %B Physical Review A %V 88 %8 2013/9/12 %G eng %U http://arxiv.org/abs/1308.4449v1 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.88.033615 %0 Journal Article %J Communications in Mathematical Physics %D 2013 %T A framework for bounding nonlocality of state discrimination %A Andrew M. Childs %A Debbie Leung %A Laura Mancinska %A Maris Ozols %X We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement" [BDF+99], we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question [BDF+99]. %B Communications in Mathematical Physics %V 323 %P 1121 - 1153 %8 2013/9/4 %G eng %U http://arxiv.org/abs/1206.5822v1 %N 3 %! Commun. Math. Phys. %R 10.1007/s00220-013-1784-0 %0 Journal Article %J Physical Review A %D 2013 %T Individual Addressing in Quantum Computation through Spatial Refocusing %A Chao Shen %A Zhe-Xuan Gong %A Luming Duan %X Separate addressing of individual qubits is a challenging requirement for scalable quantum computation, and crosstalk between operations on neighboring qubits remains as a significant source of noise for current experimental implementation of multi-qubit platforms. We propose a scheme based on spatial refocusing from interference of several coherent laser beams to significantly reduce the crosstalk noise for any type of quantum gates. A general framework is developed for the spatial refocusing technique, in particular with practical Gaussian beams, and we show under typical experimental conditions, the crosstalk-induced infidelity of quantum gates can be reduced by several orders of magnitude with a moderate cost of a few correction laser beams. %B Physical Review A %V 88 %8 2013/11/21 %G eng %U http://arxiv.org/abs/1305.2798v3 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.88.052325 %0 Journal Article %J Journal of Mathematical Physics %D 2013 %T Interpolatability distinguishes LOCC from separable von Neumann measurements %A Andrew M. Childs %A Debbie Leung %A Laura Mancinska %A Maris Ozols %X Local operations with classical communication (LOCC) and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement. Separable operations are strictly more powerful than LOCC, but no simple explanation of this phenomenon is known. We show that, in the case of von Neumann measurements, the ability to interpolate measurements is an operational principle that sets apart LOCC and separable operations. %B Journal of Mathematical Physics %V 54 %P 112204 %8 2013/06/25 %G eng %U http://arxiv.org/abs/1306.5992v1 %N 11 %! J. Math. Phys. %R 10.1063/1.4830335 %0 Journal Article %J Lecture Notes in Computer Science %D 2013 %T An Introduction to Quantum Programming in Quipper %A Alexander S. Green %A Peter LeFanu Lumsdaine %A Neil J. Ross %A Peter Selinger %A Benoît Valiron %X Quipper is a recently developed programming language for expressing quantum computations. This paper gives a brief tutorial introduction to the language, through a demonstration of how to make use of some of its key features. We illustrate many of Quipper's language features by developing a few well known examples of Quantum computation, including quantum teleportation, the quantum Fourier transform, and a quantum circuit for addition. %B Lecture Notes in Computer Science %V 7948 %P 110-124 %8 2013/07/05 %@ 978-3-642-38986-3 %G eng %U http://arxiv.org/abs/1304.5485v1 %! Lecture Notes in Computer Science 7948:110-124 %R 10.1007/978-3-642-38986-3_10 %0 Journal Article %J Molecular Physics %D 2013 %T Kitaev honeycomb and other exotic spin models with polar molecules %A Alexey V. Gorshkov %A Kaden R. A. Hazzard %A Ana Maria Rey %X We show that ultracold polar molecules pinned in an optical lattice can be used to access a variety of exotic spin models, including the Kitaev honeycomb model. Treating each molecule as a rigid rotor, we use DC electric and microwave fields to define superpositions of rotational levels as effective spin degrees of freedom, while dipole-dipole interactions give rise to interactions between the spins. In particular, we show that, with sufficient microwave control, the interaction between two spins can be written as a sum of five independently controllable Hamiltonian terms proportional to the five rank-2 spherical harmonics Y_{2,q}(theta,phi), where (theta,phi) are the spherical coordinates of the vector connecting the two molecules. To demonstrate the potential of this approach beyond the simplest examples studied in [S. R. Manmana et al., arXiv:1210.5518v2], we focus on the realization of the Kitaev honeycomb model, which can support exotic non-Abelian anyonic excitations. We also discuss the possibility of generating spin Hamiltonians with arbitrary spin S, including those exhibiting SU(N=2S+1) symmetry. %B Molecular Physics %V 111 %P 1908 - 1916 %8 2013/01/01 %G eng %U http://arxiv.org/abs/1301.5636v1 %N 12-13 %! Molecular Physics %R 10.1080/00268976.2013.800604 %0 Journal Article %J MultiLing (Workshop on Multilingual Multi-document Summarization) %D 2013 %T Multilingual Summarization: Dimensionality Reduction and a Step Towards Optimal Term Coverage %A John M. Conroy %A Sashka T. Davis %A Jeff Kubina %A Yi-Kai Liu %A Dianne P. O'Leary %A Judith D. Schlesinger %X In this paper we present three term weighting approaches for multi-lingual document summarization and give results on the DUC 2002 data as well as on the 2013 Multilingual Wikipedia feature articles data set. We introduce a new intervalbounded nonnegative matrix factorization. We use this new method, latent semantic analysis (LSA), and latent Dirichlet allocation (LDA) to give three term-weighting methods for multi-document multi-lingual summarization. Results on DUC and TAC data, as well as on the MultiLing 2013 data, demonstrate that these methods are very promising, since they achieve oracle coverage scores in the range of humans for 6 of the 10 test languages. Finally, we present three term weighting approaches for the MultiLing13 single document summarization task on the Wikipedia featured articles. Our submissions signifi- cantly outperformed the baseline in 19 out of 41 languages. %B MultiLing (Workshop on Multilingual Multi-document Summarization) %P 55-63 %8 2013/08/09 %G eng %U http://aclweb.org/anthology/W/W13/W13-3108.pdf %0 Journal Article %D 2013 %T A noise inequality for classical forces %A Dvir Kafri %A J. M. Taylor %X Lorentz invariance requires local interactions, with force laws such as the Coulomb interaction arising via virtual exchange of force carriers such as photons. Many have considered the possibility that, at long distances or large mass scales, this process changes in some way to lead to classical behavior. Here we hypothesize that classical behavior could be due to an inability of some force carriers to convey entanglement, a characteristic measure of nonlocal, quantum behavior. We then prove that there exists a local test that allows one to verify entanglement generation, falsifying our hypothesis. Crucially, we show that noise measurements can directly verify entanglement generation. This provides a step forward for a wide variety of experimental systems where traditional entanglement tests are challenging, including entanglement generation by gravity alone between macroscopic torsional oscillators. %8 2013/11/18 %G eng %U http://arxiv.org/abs/1311.4558v1 %0 Journal Article %J Physical Review A %D 2013 %T Non-equilibrium dynamics of Ising models with decoherence: an exact solution %A Michael Foss-Feig %A Kaden R. A. Hazzard %A John J. Bollinger %A Ana Maria Rey %X The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics: Decoherence can degrade correlations, but can also give rise to a variety of rich dynamical and steady-state behaviors. We obtain an exact analytic solution for the non-equilibrium dynamics of Ising models with arbitrary interactions and subject to the most general form of local Markovian decoherence. Our solution shows that decoherence affects the relaxation of observables more than predicted by single-particle considerations. It also reveals a dynamical phase transition, specifically a Hopf bifurcation, which is absent at the single-particle level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems. %B Physical Review A %V 87 %8 2013/4/3 %G eng %U http://arxiv.org/abs/1209.5795v2 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.87.042101 %0 Journal Article %J Physical Review A %D 2013 %T Optimal entanglement-assisted one-shot classical communication %A Hemenway, Brett %A Carl Miller %A Shi, Yaoyun %A Wootters, Mary %XThe *one-shot success probability* of a noisy classical channel for transmitting one classical bit is the optimal probability with which the bit can be successfully sent via a single use of the channel. Prevedel *et al.* [Phys. Rev. Lett. 106, 110505 (2011)] recently showed that for a specific channel, this quantity can be increased if the parties using the channel share an entangled quantum state. In this paper, we characterize the optimal entanglement-assisted protocols in terms of the radius of a set of operators associated with the channel. This characterization can be used to construct optimal entanglement-assisted protocols for a given classical channel and to prove the limits of such protocols. As an example, we show that the Prevedel *et al.* protocol is optimal for two-qubit entanglement. We also prove some tight upper bounds on the improvement that can be obtained from quantum and nonsignaling correlations.

Self-testing a quantum apparatus means verifying the existence of a certain quantum state as well as the effect of the associated measuring devices based only on the statistics of the measurement outcomes. Robust (i.e., error-tolerant) self-testing quantum apparatuses are critical building blocks for quantum cryptographic protocols that rely on imperfect or untrusted devices. We devise a general scheme for proving optimal robust self-testing properties for tests based on nonlocal binary XOR games. We offer some simplified proofs of known results on self-testing, and also prove some new results.

%B 8th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2013 %I Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing %V 22 %P 254–262 %G eng %R 10.4230/LIPIcs.TQC.2013.254 %0 Journal Article %J Physical Review B %D 2013 %T Preparation of Non-equilibrium Nuclear Spin States in Double Quantum Dots %A Michael Gullans %A J. J. Krich %A J. M. Taylor %A B. I. Halperin %A M. D. Lukin %X We theoretically study the dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. In our prior work [Phys. Rev. Lett. 104, 226807 (2010)] we identified three regimes of long-term dynamics, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. In particular, when the dots are different sizes we found that the Overhauser field becomes larger in the smaller dot. Here we present a detailed theoretical analysis of these problems including a model of the polarization dynamics and the development of a new numerical method to efficiently simulate semiclassical central-spin problems. When nuclear spin noise is included, the results agree with our prior work indicating that large difference fields and dark states are stable configurations, while the elimination of the difference field is unstable; however, in the absence of noise we find all three steady states are achieved depending on parameters. These results are in good agreement with dynamic nuclear polarization experiments in double quantum dots. %B Physical Review B %V 88 %8 2013/7/15 %G eng %U http://arxiv.org/abs/1212.6953v3 %N 3 %! Phys. Rev. B %R 10.1103/PhysRevB.88.035309 %0 Journal Article %J New Journal of Physics %D 2013 %T Prethermalization and dynamical transition in an isolated trapped ion spin chain %A Zhe-Xuan Gong %A L. -M. Duan %X We propose an experimental scheme to observe prethermalization and dynamical transition in one-dimensional XY spin chain with long range interaction and inhomogeneous lattice spacing, which can be readily implemented with the recently developed trapped-ion quantum simulator. Local physical observables are found to relax to prethermal values at intermediate time scale, followed by complete relaxation to thermal values at much longer time. The physical origin of prethermalization is explained by spotting a non-trivial structure in lower half of the energy spectrum. The dynamical behavior of the system is shown to cross difference phases when the interaction range is continuously tuned, indicating the existence of dynamical phase transition. %B New Journal of Physics %V 15 %P 113051 %8 2013/11/26 %G eng %U http://arxiv.org/abs/1305.0985v1 %N 11 %! New J. Phys. %R 10.1088/1367-2630/15/11/113051 %0 Journal Article %J Journal of Mathematical Physics %D 2013 %T Product Formulas for Exponentials of Commutators %A Andrew M. Childs %A Nathan Wiebe %X We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate unitary exponentials of (possibly nested) commutators using exponentials of the elementary operators, and we upper bound the number of elementary exponentials needed to implement the desired operation within a given error tolerance. By presenting an algorithm for quantum search using evolution according to a commutator, we show that the scaling of the number of exponentials in our product formulas with the evolution time is nearly optimal. Finally, we discuss applications of our product formulas to quantum control and to implementing anticommutators, providing new methods for simulating many-body interaction Hamiltonians. %B Journal of Mathematical Physics %V 54 %P 062202 %8 2013/02/07 %G eng %U http://arxiv.org/abs/1211.4945v2 %N 6 %! J. Math. Phys. %R 10.1063/1.4811386 %0 Journal Article %J Physical Review A %D 2013 %T Quadrature interferometry for nonequilibrium ultracold bosons in optical lattices %A Eite Tiesinga %A Philip R. Johnson %X We develop an interferometric technique for making time-resolved measurements of field-quadrature operators for nonequilibrium ultracold bosons in optical lattices. The technique exploits the internal state structure of magnetic atoms to create two subsystems of atoms in different spin states and lattice sites. A Feshbach resonance turns off atom-atom interactions in one spin subsystem, making it a well-characterized reference state, while atoms in the other subsystem undergo nonequilibrium dynamics for a variable hold time. Interfering the subsystems via a second beam-splitting operation, time-resolved quadrature measurements on the interacting atoms are obtained by detecting relative spin populations. The technique can provide quadrature measurements for a variety of Hamiltonians and lattice geometries (e.g., cubic, honeycomb, superlattices), including systems with tunneling, spin-orbit couplings using artificial gauge fields, and higher-band effects. Analyzing the special case of a deep lattice with negligible tunneling, we obtain the time evolution of both quadrature observables and their fluctuations. As a second application, we show that the interferometer can be used to measure atom-atom interaction strengths with super-Heisenberg scaling n^(-3/2) in the mean number of atoms per lattice site n, and standard quantum limit scaling M^(-1/2) in the number of lattice sites M. In our analysis, we require M >> 1 and for realistic systems n is small, and therefore the scaling in total atom number N = nM is below the Heisenberg limit; nevertheless, measurements testing the scaling behaviors for interaction-based quantum metrologies should be possible in this system. %B Physical Review A %V 87 %8 2013/1/22 %G eng %U http://arxiv.org/abs/1212.1193v2 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.87.013423 %0 Journal Article %J Chicago Journal of Theoretical Computer Science %D 2013 %T Quantum Adversary (Upper) Bound %A Shelby Kimmel %X We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity without producing an algorithm. For example, we describe an oracle problem which we prove (non-constructively) can be solved in $O(1)$ queries, where the previous best quantum algorithm uses a polylogarithmic number of queries. We then give an explicit $O(1)$-query algorithm for this problem based on span programs. %B Chicago Journal of Theoretical Computer Science %V 19 %P 1 - 14 %8 2013/04/05 %G eng %U http://arxiv.org/abs/1101.0797v5 %N 1 %! Chicago J. of Theoretical Comp. Sci. %R 10.4086/cjtcs.2013.004 %0 Journal Article %J Physical Review Letters %D 2013 %T Quantum Catalysis of Magnetic Phase Transitions in a Quantum Simulator %A Philip Richerme %A Crystal Senko %A Simcha Korenblit %A Jacob Smith %A Aaron Lee %A Rajibul Islam %A Wesley C. Campbell %A Christopher Monroe %X We control quantum fluctuations to create the ground state magnetic phases of a classical Ising model with a tunable longitudinal magnetic field using a system of 6 to 10 atomic ion spins. Due to the long-range Ising interactions, the various ground state spin configurations are separated by multiple first-order phase transitions, which in our zero temperature system cannot be driven by thermal fluctuations. We instead use a transverse magnetic field as a quantum catalyst to observe the first steps of the complete fractal devil's staircase, which emerges in the thermodynamic limit and can be mapped to a large number of many-body and energy-optimization problems. %B Physical Review Letters %V 111 %8 2013/9/5 %G eng %U http://arxiv.org/abs/1303.6983v2 %N 10 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.111.100506 %0 Journal Article %J Physical Review A %D 2013 %T Quantum Cherenkov Radiation and Non-contact Friction %A Mohammad F. Maghrebi %A Ramin Golestanian %A Mehran Kardar %X We present a number of arguments to demonstrate that a quantum analog of Cherenkov effect occurs when two dispersive objects are in relative motion. Specifically we show that two semi-infinite plates experience friction beyond a threshold velocity which, in their center-of-mass frame, is the phase speed of light within their medium. The loss in mechanical energy is radiated away through the plates before getting fully absorbed in the form of heat. By deriving various correlation functions inside and outside the two plates, we explicitly compute the radiation, and discuss its dependence on the reference frame. %B Physical Review A %V 88 %8 2013/10/21 %G eng %U http://arxiv.org/abs/1304.4909v2 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.88.042509 %0 Journal Article %J Physical Review A %D 2013 %T Quantum Logic between Remote Quantum Registers %A Norman Y. Yao %A Zhe-Xuan Gong %A Chris R. Laumann %A Steven D. Bennett %A L. -M. Duan %A Mikhail D. Lukin %A Liang Jiang %A Alexey V. Gorshkov %X We analyze two approaches to quantum state transfer in solid-state spin systems. First, we consider unpolarized spin-chains and extend previous analysis to various experimentally relevant imperfections, including quenched disorder, dynamical decoherence, and uncompensated long range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing which exploits all of the spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate "dark" spin qubits significantly raise the error threshold for robust operation. Finally, as an example, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated Nitrogen-Vacancy registers in diamond; numerical simulations confirm that high fidelity gates are achievable even in the presence of moderate disorder. %B Physical Review A %V 87 %8 2013/2/6 %G eng %U http://arxiv.org/abs/1206.0014v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.87.022306 %0 Journal Article %J Science %D 2013 %T A quantum many-body spin system in an optical lattice clock %A M J Martin %A Bishof, M %A Swallows, M D %A X Zhang %A C Benko %A J von-Stecher %A Alexey V. Gorshkov %A Rey, A M %A Jun Ye %B Science %V 341 %P 632 %G eng %U http://www.sciencemag.org/content/341/6146/632.abstract %0 Journal Article %J Opt. Photonics News %D 2013 %T Quantum Nonlinear Optics: Strongly Interacting Photons %A Firstenberg, O %A Lukin, M D %A Peyronel, T %A Liang, Q -Y %A Vuletic, V %A Alexey V. Gorshkov %A Hofferberth, S %A Pohl, T %B Opt. Photonics News %V 24 %P 48 %G eng %U http://www.osa-opn.org/abstract.cfm?URI=opn-24-12-48 %0 Journal Article %J ACM SIGPLAN Notices %D 2013 %T Quipper: A Scalable Quantum Programming Language %A Alexander S. Green %A Peter LeFanu Lumsdaine %A Neil J. Ross %A Peter Selinger %A Benoît Valiron %XThe field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higher-order quantum programming language. Quipper has been used to program a diverse set of non-trivial quantum algorithms, and can generate quantum gate representations using trillions of gates. It is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware. Quipper has proven effective and easy to use, and opens the door towards using formal methods to analyze quantum algorithms.

%B ACM SIGPLAN Notices %V 48 %P 333-342 %8 2013/06/23 %G eng %U http://arxiv.org/abs/1304.3390v1 %N 6 %! SIGPLAN Not. %R 10.1145/2499370.2462177 %0 Journal Article %J Physical Review Letters %D 2013 %T Realizing Fractional Chern Insulators with Dipolar Spins %A Norman Y. Yao %A Alexey V. Gorshkov %A Chris R. Laumann %A Andreas M. Läuchli %A Jun Ye %A Mikhail D. Lukin %X Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the \nu=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultra-cold polar molecules trapped in a deep optical lattice. While the orbital motion of the molecules is pinned, at finite densities, the rotational excitations form a fractional Chern insulator. We present a detailed experimental blueprint for KRb, and demonstrate that the energetics are consistent with near-term capabilities. Prospects for the realization of such phases in solid-state dipolar systems are discussed as are their possible applications. %B Physical Review Letters %V 110 %8 2013/4/29 %G eng %U http://arxiv.org/abs/1212.4839v1 %N 18 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.110.185302 %0 Journal Article %J Physical Review Letters %D 2013 %T The Resonant Exchange Qubit %A J. Medford %A J. Beil %A J. M. Taylor %A E. I. Rashba %A H. Lu %A A. C. Gossard %A C. M. Marcus %X We introduce a solid-state qubit in which exchange interactions among confined electrons provide both the static longitudinal field and the oscillatory transverse field, allowing rapid and full qubit control via rf gate-voltage pulses. We demonstrate two-axis control at a detuning sweet-spot, where leakage due to hyperfine coupling is suppressed by the large exchange gap. A {\pi}/2-gate time of 2.5 ns and a coherence time of 19 {\mu}s, using multi-pulse echo, are also demonstrated. Model calculations that include effects of hyperfine noise are in excellent quantitative agreement with experiment. %B Physical Review Letters %V 111 %8 2013/7/31 %G eng %U http://arxiv.org/abs/1304.3413v2 %N 5 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.111.050501 %0 Journal Article %J Physical Review D %D 2013 %T A Scattering Approach to the Dynamical Casimir Effect %A Mohammad F. Maghrebi %A Ramin Golestanian %A Mehran Kardar %X We develop a unified scattering approach to dynamical Casimir problems which can be applied to both accelerating boundaries, as well as dispersive objects in relative motion. A general (trace) formula is derived for the radiation from accelerating boundaries. Applications are provided for objects with different shapes in various dimensions, and undergoing rotational or linear motion. Within this framework, photon generation is discussed in the context of a modulated optical mirror. For dispersive objects, we find general results solely in terms of the scattering matrix. Specifically, we discuss the vacuum friction on a rotating object, and the friction on an atom moving parallel to a surface. %B Physical Review D %V 87 %8 2013/1/7 %G eng %U http://arxiv.org/abs/1210.1842v2 %N 2 %! Phys. Rev. D %R 10.1103/PhysRevD.87.025016 %0 Journal Article %J Nature Nanotechnology %D 2013 %T Self-Consistent Measurement and State Tomography of an Exchange-Only Spin Qubit %A J. Medford %A J. Beil %A J. M. Taylor %A S. D. Bartlett %A A. C. Doherty %A E. I. Rashba %A D. P. DiVincenzo %A H. Lu %A A. C. Gossard %A C. M. Marcus %X We report initialization, complete electrical control, and single-shot readout of an exchange-only spin qubit. Full control via the exchange interaction is fast, yielding a demonstrated 75 qubit rotations in under 2 ns. Measurement and state tomography are performed using a maximum-likelihood estimator method, allowing decoherence, leakage out of the qubit state space, and measurement fidelity to be quantified. The methods developed here are generally applicable to systems with state leakage, noisy measurements, and non-orthogonal control axes. %B Nature Nanotechnology %V 8 %P 654 - 659 %8 2013/9/1 %G eng %U http://arxiv.org/abs/1302.1933v1 %N 9 %! Nature Nanotech %R 10.1038/nnano.2013.168 %0 Journal Article %J Physical Review Letters %D 2013 %T Single-photon nonlinear optics with graphene plasmons %A Michael Gullans %A D. E. Chang %A F. H. L. Koppens %A F. J. García de Abajo %A M. D. Lukin %X We show that it is possible to realize significant nonlinear optical interactions at the few photon level in graphene nanostructures. Our approach takes advantage of the electric field enhancement associated with the strong confinement of graphene plasmons and the large intrinsic nonlinearity of graphene. Such a system could provide a powerful platform for quantum nonlinear optical control of light. As an example, we consider an integrated optical device that exploits this large nonlinearity to realize a single photon switch. %B Physical Review Letters %V 111 %8 2013/12/11 %G eng %U http://arxiv.org/abs/1309.2651v3 %N 24 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.111.247401 %0 Journal Article %J Physical Review A %D 2013 %T Soliton dynamics of an atomic spinor condensate on a Ring Lattice %A Indubala I Satija %A Carlos L. Pando %A Eite Tiesinga %X We study the dynamics of macroscopically-coherent matter waves of an ultra-cold atomic spin-one or spinor condensate on a ring lattice of six sites and demonstrate a novel type of spatio-temporal internal Josephson effect. Using a discrete solitary mode of uncoupled spin components as an initial condition, the time evolution of this many-body system is found to be characterized by two dominant frequencies leading to quasiperiodic dynamics at various sites. The dynamics of spatially-averaged and spin-averaged degrees of freedom, however, is periodic enabling an unique identification of the two frequencies. By increasing the spin-dependent atom-atom interaction strength we observe a resonance state, where the ratio of the two frequencies is a characteristic integer multiple and the spin-and-spatial degrees of freedom oscillate in "unison". Crucially, this resonant state is found to signal the onset to chaotic dynamics characterized by a broad band spectrum. In a ferromagnetic spinor condensate with attractive spin-dependent interactions, the resonance is accompanied by a transition from oscillatory- to rotational-type dynamics as the time evolution of the relative phase of the matter wave of the individual spin projections changes from bounded to unbounded. %B Physical Review A %V 87 %8 2013/3/6 %G eng %U http://arxiv.org/abs/1301.5851v1 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.87.033608 %0 Journal Article %J Physical Review Letters %D 2013 %T Spinor dynamics in an antiferromagnetic spin-1 thermal Bose gas %A Hyewon K. Pechkis %A Jonathan P. Wrubel %A Arne Schwettmann %A Paul F. Griffin %A Ryan Barnett %A Eite Tiesinga %A Paul D. Lett %X We present experimental observations of coherent spin-population oscillations in a cold thermal, Bose gas of spin-1 sodium-23 atoms. The population oscillations in a multi-spatial-mode thermal gas have the same behavior as those observed in a single-spatial-mode antiferromagnetic spinor Bose Einstein condensate. We demonstrate this by showing that the two situations are described by the same dynamical equations, with a factor of two change in the spin-dependent interaction coefficient, which results from the change to particles with distinguishable momentum states in the thermal gas. We compare this theory to the measured spin population evolution after times up to a few hundreds of ms, finding quantitative agreement with the amplitude and period. We also measure the damping time of the oscillations as a function of magnetic field. %B Physical Review Letters %V 111 %8 2013/7/9 %G eng %U http://arxiv.org/abs/1306.4255v1 %N 2 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.111.025301 %0 Journal Article %J 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013) %D 2013 %T Symmetries of Codeword Stabilized Quantum Codes %A Salman Beigi %A Jianxin Chen %A Markus Grassl %A Zhengfeng Ji %A Qiang Wang %A Bei Zeng %X Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general framework for constructing quantum error-correcting codes known to date. A CWS code Q can be represented by a self-dual additive code S and a classical code C, i.,e., Q=(S,C), however this representation is in general not unique. We show that for any CWS code Q with certain permutation symmetry, one can always find a self-dual additive code S with the same permutation symmetry as Q such that Q=(S,C). As many good CWS codes have been found by starting from a chosen S, this ensures that when trying to find CWS codes with certain permutation symmetry, the choice of S with the same symmetry will suffice. A key step for this result is a new canonical representation for CWS codes, which is given in terms of a unique decomposition as union stabilizer codes. For CWS codes, so far mainly the standard form (G,C) has been considered, where G is a graph state. We analyze the symmetry of the corresponding graph of G, which in general cannot possess the same permutation symmetry as Q. We show that it is indeed the case for the toric code on a square lattice with translational symmetry, even if its encoding graph can be chosen to be translational invariant. %B 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013) %V 22 %P 192-206 %8 2013/03/28 %G eng %U http://arxiv.org/abs/1303.7020v2 %R 10.4230/LIPIcs.TQC.2013.192 %0 Journal Article %J Physical Review A %D 2013 %T Testing quantum expanders is co-QMA-complete %A Adam D. Bookatz %A Stephen P. Jordan %A Yi-Kai Liu %A Pawel Wocjan %X A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap) of a quantum expander. We show that this problem is co-QMA-complete. This has applications to testing randomized constructions of quantum expanders, and studying thermalization of open quantum systems. %B Physical Review A %V 87 %8 2013/4/15 %G eng %U http://arxiv.org/abs/1210.0787v2 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.87.042317 %0 Journal Article %D 2013 %T A Time-Efficient Quantum Walk for 3-Distinctness Using Nested Updates %A Andrew M. Childs %A Stacey Jeffery %A Robin Kothari %A Frederic Magniez %X We present an extension to the quantum walk search framework that facilitates quantum walks with nested updates. We apply it to give a quantum walk algorithm for 3-Distinctness with query complexity ~O(n^{5/7}), matching the best known upper bound (obtained via learning graphs) up to log factors. Furthermore, our algorithm has time complexity ~O(n^{5/7}), improving the previous ~O(n^{3/4}). %8 2013/02/28 %G eng %U http://arxiv.org/abs/1302.7316v1 %0 Journal Article %J Physical Review B %D 2013 %T Topological phases in ultracold polar-molecule quantum magnets %A Salvatore R. Manmana %A E. M. Stoudenmire %A Kaden R. A. Hazzard %A Ana Maria Rey %A Alexey V. Gorshkov %X We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin S >= 1/2 and with interactions featuring a direction-dependent spin anisotropy. This is achieved by encoding the effective spin degrees of freedom in microwave-dressed rotational states of the molecules and by coupling the spins through dipolar interactions. We demonstrate how one of the experimentally most accessible anisotropies stabilizes symmetry protected topological phases in spin ladders. Using the numerically exact density matrix renormalization group method, we find that these interacting phases -- previously studied only in the nearest-neighbor case -- survive in the presence of long-range dipolar interactions. We also show how to use our approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb models. Experimental detection schemes and imperfections are discussed. %B Physical Review B %V 87 %8 2013/2/26 %G eng %U http://arxiv.org/abs/1210.5518v2 %N 8 %! Phys. Rev. B %R 10.1103/PhysRevB.87.081106 %0 Journal Article %J Nature Communications %D 2013 %T Topologically Protected Quantum State Transfer in a Chiral Spin Liquid %A Norman Y. Yao %A Chris R. Laumann %A Alexey V. Gorshkov %A Hendrik Weimer %A Liang Jiang %A J. Ignacio Cirac %A Peter Zoller %A Mikhail D. Lukin %X Topology plays a central role in ensuring the robustness of a wide variety of physical phenomena. Notable examples range from the robust current carrying edge states associated with the quantum Hall and the quantum spin Hall effects to proposals involving topologically protected quantum memory and quantum logic operations. Here, we propose and analyze a topologically protected channel for the transfer of quantum states between remote quantum nodes. In our approach, state transfer is mediated by the edge mode of a chiral spin liquid. We demonstrate that the proposed method is intrinsically robust to realistic imperfections associated with disorder and decoherence. Possible experimental implementations and applications to the detection and characterization of spin liquid phases are discussed. %B Nature Communications %V 4 %P 1585 %8 2013/3/12 %G eng %U http://arxiv.org/abs/1110.3788v1 %! Nat Comms %R 10.1038/ncomms2531 %0 Journal Article %J Physical Review A %D 2013 %T Uniqueness of Quantum States Compatible with Given Measurement Results %A Jianxin Chen %A Hillary Dawkins %A Zhengfeng Ji %A Nathaniel Johnston %A David Kribs %A Frederic Shultz %A Bei Zeng %X We discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it is known that for a d-dimensional Hilbert space, there exists a set of 4d-5 observables that uniquely determines any pure state. We show that for case (2), 5d-7 observables suffice to uniquely determine any pure state. Thus there is a gap between the results for (1) and (2), and we give some examples to illustrate this. The case of observables corresponding to reduced density matrices (RDMs) of a multipartite system is also discussed, where we improve known bounds on local dimensions for case (2) in which almost all pure states are uniquely determined by their RDMs. We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low rank quantum states. %B Physical Review A %V 88 %8 2013/7/11 %G eng %U http://arxiv.org/abs/1212.3503v2 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.88.012109 %0 Journal Article %J Science %D 2013 %T Universal computation by multi-particle quantum walk %A Andrew M. Childs %A David Gosset %A Zak Webb %X A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we consider a generalization of quantum walk to systems with more than one walker. A continuous-time multi-particle quantum walk is generated by a time-independent Hamiltonian with a term corresponding to a single-particle quantum walk for each particle, along with an interaction term. Multi-particle quantum walk includes a broad class of interacting many-body systems such as the Bose-Hubbard model and systems of fermions or distinguishable particles with nearest-neighbor interactions. We show that multi-particle quantum walk is capable of universal quantum computation. Since it is also possible to efficiently simulate a multi-particle quantum walk of the type we consider using a universal quantum computer, this model exactly captures the power of quantum computation. In principle our construction could be used as an architecture for building a scalable quantum computer with no need for time-dependent control. %B Science %V 339 %P 791 - 794 %8 2013/02/14 %G eng %U http://arxiv.org/abs/1205.3782v2 %N 6121 %! Science %R 10.1126/science.1229957 %0 Journal Article %D 2013 %T Universal Entanglers for Bosonic and Fermionic Systems %A Joel Klassen %A Jianxin Chen %A Bei Zeng %X A universal entangler (UE) is a unitary operation which maps all pure product states to entangled states. It is known that for a bipartite system of particles $1,2$ with a Hilbert space $\mathbb{C}^{d_1}\otimes\mathbb{C}^{d_2}$, a UE exists when $\min{(d_1,d_2)}\geq 3$ and $(d_1,d_2)\neq (3,3)$. It is also known that whenever a UE exists, almost all unitaries are UEs; however to verify whether a given unitary is a UE is very difficult since solving a quadratic system of equations is NP-hard in general. This work examines the existence and construction of UEs of bipartite bosonic/fermionic systems whose wave functions sit in the symmetric/antisymmetric subspace of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$. The development of a theory of UEs for these types of systems needs considerably different approaches from that used for UEs of distinguishable systems. This is because the general entanglement of identical particle systems cannot be discussed in the usual way due to the effect of (anti)-symmetrization which introduces "pseudo entanglement" that is inaccessible in practice. We show that, unlike the distinguishable particle case, UEs exist for bosonic/fermionic systems with Hilbert spaces which are symmetric (resp. antisymmetric) subspaces of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$ if and only if $d\geq 3$ (resp. $d\geq 8$). To prove this we employ algebraic geometry to reason about the different algebraic structures of the bosonic/fermionic systems. Additionally, due to the relatively simple coherent state form of unentangled bosonic states, we are able to give the explicit constructions of two bosonic UEs. Our investigation provides insight into the entanglement properties of systems of indisitinguishable particles, and in particular underscores the difference between the entanglement structures of bosonic, fermionic and distinguishable particle systems. %8 2013/05/31 %G eng %U http://arxiv.org/abs/1305.7489v1 %0 Journal Article %J Quantum Information and Computation %D 2012 %T Achieving perfect completeness in classical-witness quantum Merlin-Arthur proof systems %A Stephen P. Jordan %A Hirotada Kobayashi %A Daniel Nagaj %A Harumichi Nishimura %X This paper proves that classical-witness quantum Merlin-Arthur proof systems can achieve perfect completeness. That is, QCMA = QCMA1. This holds under any gate set with which the Hadamard and arbitrary classical reversible transformations can be exactly implemented, e.g., {Hadamard, Toffoli, NOT}. The proof is quantumly nonrelativizing, and uses a simple but novel quantum technique that additively adjusts the success probability, which may be of independent interest. %B Quantum Information and Computation %V 12 %P 461-471 %8 2012/05/01 %G eng %U http://arxiv.org/abs/1111.5306v2 %N 5-6 %! Quantum Information and Computation Vol. 12 No. 5/6 pg. 461-471 (2012) %0 Journal Article %D 2012 %T Algorithmic Cooling of a Quantum Simulator %A Dvir Kafri %A J. M. Taylor %X Controlled quantum mechanical devices provide a means of simulating more complex quantum systems exponentially faster than classical computers. Such "quantum simulators" rely heavily upon being able to prepare the ground state of Hamiltonians, whose properties can be used to calculate correlation functions or even the solution to certain classical computations. While adiabatic preparation remains the primary means of producing such ground states, here we provide a different avenue of preparation: cooling to the ground state via simulated dissipation. This is in direct analogy to contemporary efforts to realize generalized forms of simulated annealing in quantum systems. %8 2012/07/30 %G eng %U http://arxiv.org/abs/1207.7111v1 %0 Journal Article %J Physical Review Letters %D 2012 %T Anisotropy induced Feshbach resonances in a quantum dipolar gas of magnetic atoms %A Alexander Petrov %A Eite Tiesinga %A Svetlana Kotochigova %X We explore the anisotropic nature of Feshbach resonances in the collision between ultracold magnetic submerged-shell dysprosium atoms, which can only occur due to couplings to rotating bound states. This is in contrast to well-studied alkali-metal atom collisions, where most Feshbach resonances are hyperfine induced and due to rotation-less bound states. Our novel first-principle coupled-channel calculation of the collisions between open-4f-shell spin-polarized bosonic dysprosium reveals a striking correlation between the anisotropy due to magnetic dipole-dipole and electrostatic interactions and the Feshbach spectrum as a function of an external magnetic field. Over a 20 mT magnetic field range we predict about a dozen Feshbach resonances and show that the resonance locations are exquisitely sensitive to the dysprosium isotope. %B Physical Review Letters %V 109 %8 2012/9/7 %G eng %U http://arxiv.org/abs/1203.4172v1 %N 10 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.109.103002 %0 Journal Article %J Proceedings, ITCS %D 2012 %T On Beating the Hybrid Argument %A Bill Fefferman %A Ronen Shaltiel %A Christopher Umans %A Emanuele Viola %X The hybrid argument allows one to relate the distinguishability of a distribution (from uniform) to the predictability of individual bits given a prefix. The argument incurs a loss of a factor k equal to the bit-length of the distributions: -distinguishability implies only /k-predictability. This paper studies the consequences of avoiding this loss – what we call “beating the hybrid argument” – and develops new proof techniques that circumvent the loss in certain natural settings. Specifically, we obtain the following results: 1. We give an instantiation of the Nisan-Wigderson generator (JCSS ’94) that can be broken by quantum computers, and that is o(1)-unpredictable against AC0 . This is not enough to imply indistinguishability via the hybrid argument because of the hybrid-argument loss; nevertheless, we conjecture that this generator indeed fools AC0 , and we prove this statement for a simplified version of the problem. Our conjecture implies the existence of an oracle relative to which BQP is not in the PH, a longstanding open problem. 2. We show that the “INW” generator by Impagliazzo, Nisan, and Wigderson (STOC ’94) with seed length O(log n log log n) produces a distribution that is 1/ log n-unpredictable against poly-logarithmic width (general) read-once oblivious branching programs. Thus avoiding the hybrid-argument loss would lead to a breakthrough in generators against small space. 3. We study pseudorandom generators obtained from a hard function by repeated sampling. We identify a property of functions, “resamplability,” that allows us to beat the hybrid argument, leading to new pseudorandom generators for AC0 [p] and similar classes. Although the generators have sub-linear stretch, they represent the best-known generators for these classes. Thus we establish that “beating” or bypassing the hybrid argument would have two significant consequences in complexity, and we take steps toward that goal by developing techniques that indeed beat the hybrid argument in related (but simpler) settings, leading to best-known PRGs for certain complexity classes. %B Proceedings, ITCS %V 9 %P 809-843 %8 2013/11/14 %G eng %U http://users.cms.caltech.edu/~umans/papers/FSUV10.pdf %0 Journal Article %J New J. Phys. %D 2012 %T Cavity QED with atomic mirrors %A D E Chang %A Jiang, L %A Alexey V. Gorshkov %A H J Kimble %B New J. Phys. %V 14 %P 063003 %G eng %U http://iopscience.iop.org/1367-2630/14/6/063003/ %0 Journal Article %J Journal of Mathematical Physics %D 2012 %T Comment on some results of Erdahl and the convex structure of reduced density matrices %A Jianxin Chen %A Zhengfeng Ji %A Mary Beth Ruskai %A Bei Zeng %A Duan-Lu Zhou %X In J. Math. Phys. 13, 1608-1621 (1972), Erdahl considered the convex structure of the set of $N$-representable 2-body reduced density matrices in the case of fermions. Some of these results have a straightforward extension to the $m$-body setting and to the more general quantum marginal problem. We describe these extensions, but can not resolve a problem in the proof of Erdahl's claim that every extreme point is exposed in finite dimensions. Nevertheless, we can show that when $2m \geq N$ every extreme point of the set of $N$-representable $m$-body reduced density matrices has a unique pre-image in both the symmetric and anti-symmetric setting. Moreover, this extends to the quantum marginal setting for a pair of complementary $m$-body and $(N-m)$-body reduced density matrices. %B Journal of Mathematical Physics %V 53 %P 072203 %8 2012/05/16 %G eng %U http://arxiv.org/abs/1205.3682v1 %N 7 %! J. Math. Phys. %R 10.1063/1.4736842 %0 Journal Article %J Physical Review A %D 2012 %T Correlations in excited states of local Hamiltonians %A Jianxin Chen %A Zhengfeng Ji %A Zhaohui Wei %A Bei Zeng %X Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix). %B Physical Review A %V 85 %8 2012/4/9 %G eng %U http://arxiv.org/abs/1106.1373v2 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.85.040303 %0 Journal Article %J Physical Review E %D 2012 %T The equilibrium states of open quantum systems in the strong coupling regime %A Y. Subasi %A C. H. Fleming %A J. M. Taylor %A B. L. Hu %X In this work we investigate the late-time stationary states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily relax to a Boltzmann distribution if the coupling to the thermal reservoir is non-vanishing or equivalently if the relaxation timescales are finite. Using a variety of non-equilibrium formalisms valid for non-Markovian processes, we show that starting from a product state of the closed system = system + environment, with the environment in its thermal state, the open system which results from coarse graining the environment will evolve towards an equilibrium state at late-times. This state can be expressed as the reduced state of the closed system thermal state at the temperature of the environment. For a linear (harmonic) system and environment, which is exactly solvable, we are able to show in a rigorous way that all multi-time correlations of the open system evolve towards those of the closed system thermal state. Multi-time correlations are especially relevant in the non-Markovian regime, since they cannot be generated by the dynamics of the single-time correlations. For more general systems, which cannot be exactly solved, we are able to provide a general proof that all single-time correlations of the open system evolve to those of the closed system thermal state, to first order in the relaxation rates. For the special case of a zero-temperature reservoir, we are able to explicitly construct the reduced closed system thermal state in terms of the environmental correlations. %B Physical Review E %V 86 %8 2012/12/26 %G eng %U http://arxiv.org/abs/1206.2707v1 %N 6 %! Phys. Rev. E %R 10.1103/PhysRevE.86.061132 %0 Journal Article %J Physical Review A %D 2012 %T From Ground States to Local Hamiltonians %A Jianxin Chen %A Zhengfeng Ji %A Bei Zeng %A D. L. Zhou %X Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest neighbour interactions on some type of lattices. A necessary condition for a space $V$ to be the ground-state space of some local Hamiltonian with a given interaction pattern, is that the maximally mixed state supported on $V$ is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy. However, it is unclear whether this condition is in general also sufficient. We examine the situations for the existence of such a local Hamiltonian to have $V$ satisfying the necessary condition mentioned above as its ground-state space, by linking to faces of the convex body of the local reduced states. We further discuss some methods for constructing the corresponding local Hamiltonians with given interaction patterns, mainly from physical points of view, including constructions related to perturbation methods, local frustration-free Hamiltonians, as well as thermodynamical ensembles. %B Physical Review A %V 86 %8 2012/8/30 %G eng %U http://arxiv.org/abs/1110.6583v4 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.86.022339 %0 Journal Article %J Proceedings of the 15th International Conference on Foundations of Software Science and Computation Structures %D 2012 %T Full Abstraction for Set-Based Models of the Symmetric Interaction Combinators %A Damiano Mazza %A Neil J. Ross %X The symmetric interaction combinators are a model of distributed and deterministic computation based on Lafont’s interaction nets, a special form of graph rewriting. The interest of the symmetric interaction combinators lies in their universality, that is, the fact that they may encode all other interaction net systems; for instance, several implementations of the lambda-calculus in the symmetric interaction combinators exist, related to Lamping’s sharing graphs for optimal reduction. A certain number of observational equivalences were introduced for this system, by Lafont, Fernandez and Mackie, and the first author. In this paper, we study the problem of full abstraction with respect to one of these equivalences, using a class of very simple denotational models based on pointed sets. %B Proceedings of the 15th International Conference on Foundations of Software Science and Computation Structures %V 7213 %P 316-330 %8 2012/01/01 %G eng %U https://lipn.univ-paris13.fr/~mazza/papers/CombSetSem-FOSSACS2012.pdf %0 Journal Article %J Central European Journal of Mathematics %D 2012 %T On Galilean connections and the first jet bundle %A Grant, James DE %A Brad Lackey %X We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations — sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces “laboratory” coordinate systems, and the geodesic equations in this coordinates form a system of second-order ordinary differential equations. We then show the converse — the “fundamental theorem” — that given such a coordinate system, and a system of second order ordinary differential equations, there exists regular Cartan connections yielding these, and such connections are completely determined by their torsion. %B Central European Journal of Mathematics %I Springer %V 10 %P 1889–1895 %8 2012/10/01 %G eng %0 Journal Article %J Physical Review D %D 2012 %T Gluon chain formation in presence of static charges %A Aaron Ostrander %A Santopinto, E. %A Szczepaniak, A. P. %A Vassallo, A. %X We consider the origins of the gluon chain model. The model serves as a realization of the dynamics of the chromoelectric flux between static quark-antiquark sources. The derivation is based on the large-NC limit of the Coulomb gauge Hamiltonian in the presence of a background field introduced to model magnetic charge condensation inducing electric confinement. %B Physical Review D %V 86 %P 114015 %8 2012/12/10 %G eng %U http://link.aps.org/doi/10.1103/PhysRevD.86.114015 %R 10.1103/PhysRevD.86.114015 %0 Journal Article %J Journal of Mathematical Physics %D 2012 %T Ground-State Spaces of Frustration-Free Hamiltonians %A Jianxin Chen %A Zhengfeng Ji %A David Kribs %A Zhaohui Wei %A Bei Zeng %X We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of `reduced spaces' to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set $\Theta_k$ of all the $k$-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in $\Theta_k$, called atoms, are analogs of extreme points. We study the properties of atoms in $\Theta_k$ and discuss its relationship with ground states of $k$-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in $\Theta_2$ are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in $\Theta_k$ may not be the join of atoms, indicating a richer structure for $\Theta_k$ beyond the convex structure. Our study of $\Theta_k$ deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from a new angle of reduced spaces. %B Journal of Mathematical Physics %V 53 %P 102201 %8 2012/01/01 %G eng %U http://arxiv.org/abs/1112.0762v1 %N 10 %! J. Math. Phys. %R 10.1063/1.4748527 %0 Journal Article %J Quantum Information and Computation %D 2012 %T Hamiltonian Simulation Using Linear Combinations of Unitary Operations %A Andrew M. Childs %A Nathan Wiebe %X We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation algorithms based on product formulas and, most notably, scales better with the simulation error than any known Hamiltonian simulation technique. Our main tool is a general method to nearly deterministically implement linear combinations of nearby unitary operations, which we show is optimal among a large class of methods. %B Quantum Information and Computation %V 12 %P 901-924 %8 2012/11/01 %G eng %U http://arxiv.org/abs/1202.5822v1 %N 11-12 %! Quantum Information and Computation 12 %0 Journal Article %J Journal of Mathematical Physics %D 2012 %T Levinson's theorem for graphs II %A Andrew M. Childs %A David Gosset %X We prove Levinson's theorem for scattering on an (m+n)-vertex graph with n semi-infinite paths each attached to a different vertex, generalizing a previous result for the case n=1. This theorem counts the number of bound states in terms of the winding of the determinant of the S-matrix. We also provide a proof that the bound states and incoming scattering states of the Hamiltonian together form a complete basis for the Hilbert space, generalizing another result for the case n=1. %B Journal of Mathematical Physics %V 53 %P 102207 %8 2012/11/21 %G eng %U http://arxiv.org/abs/1203.6557v2 %N 10 %! J. Math. Phys. %R 10.1063/1.4757665 %0 Journal Article %J Physical Review Letters %D 2012 %T Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice %A Amodsen Chotia %A Brian Neyenhuis %A Steven A. Moses %A Bo Yan %A Jacob P. Covey %A Michael Foss-Feig %A Ana Maria Rey %A Deborah S. Jin %A Jun Ye %X We have realized long-lived ground-state polar molecules in a 3D optical lattice, with a lifetime of up to 25 s, which is limited only by off-resonant scattering of the trapping light. Starting from a 2D optical lattice, we observe that the lifetime increases dramatically as a small lattice potential is added along the tube-shaped lattice traps. The 3D optical lattice also dramatically increases the lifetime for weakly bound Feshbach molecules. For a pure gas of Feshbach molecules, we observe a lifetime of >20 s in a 3D optical lattice; this represents a 100-fold improvement over previous results. This lifetime is also limited by off-resonant scattering, the rate of which is related to the size of the Feshbach molecule. Individually trapped Feshbach molecules in the 3D lattice can be converted to pairs of K and Rb atoms and back with nearly 100% efficiency. %B Physical Review Letters %V 108 %8 2012/2/23 %G eng %U http://arxiv.org/abs/1110.4420v1 %N 8 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.108.080405 %0 Journal Article %D 2012 %T Minimum Entangling Power is Close to Its Maximum %A Jianxin Chen %A Zhengfeng Ji %A David W Kribs %A Bei Zeng %X Given a quantum gate $U$ acting on a bipartite quantum system, its maximum (average, minimum) entangling power is the maximum (average, minimum) entanglement generation with respect to certain entanglement measure when the inputs are restricted to be product states. In this paper, we mainly focus on the 'weakest' one, i.e., the minimum entangling power, among all these entangling powers. We show that, by choosing von Neumann entropy of reduced density operator or Schmidt rank as entanglement measure, even the 'weakest' entangling power is generically very close to its maximal possible entanglement generation. In other words, maximum, average and minimum entangling powers are generically close. We then study minimum entangling power with respect to other Lipschitiz-continuous entanglement measures and generalize our results to multipartite quantum systems. As a straightforward application, a random quantum gate will almost surely be an intrinsically fault-tolerant entangling device that will always transform every low-entangled state to near-maximally entangled state. %8 2012/10/04 %G eng %U http://arxiv.org/abs/1210.1296v1 %0 Journal Article %J Physical Review Letters %D 2012 %T Nanoplasmonic Lattices for Ultracold atoms %A Michael Gullans %A T. Tiecke %A D. E. Chang %A J. Feist %A J. D. Thompson %A J. I. Cirac %A P. Zoller %A M. D. Lukin %X We propose to use sub-wavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the sub-wavelength manipulation and strong light-matter interaction associated with nano-plasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed. %B Physical Review Letters %V 109 %8 2012/12/6 %G eng %U http://arxiv.org/abs/1208.6293v3 %N 23 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.109.235309 %0 Journal Article %D 2012 %T Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt) %A Jianxin Chen %A Andreas Winter %X We demonstrate the convexity of the difference between the regularized entanglement of purification and the entropy, as a function of the state. This is proved by means of a new asymptotic protocol to prepare a state from pre-shared entanglement and by local operations only. We go on to employ this convexity property in an investigation of the additivity of the (single-copy) entanglement of purification: using numerical results for two-qubit Werner states we find strong evidence that the entanglement of purification is different from its regularization, hence that entanglement of purification is not additive. %8 2012/06/06 %G eng %U http://arxiv.org/abs/1206.1307v1 %0 Journal Article %J The Electronic Journal of Combinatorics %D 2012 %T Non-Recursively Constructible Recursive Families of Graphs %A Colleen Bouey %A Christina Graves %A Aaron Ostrander %A Gregory Palma %X In a publication by Noy and Ribó, it was shown that recursively constructible families of graphs are recursive. The authors also conjecture that the converse holds; that is, recursive families are also recursively constructible. In this paper, we provide two specific counterexamples to this conjecture, which we then extend to an infinite family of counterexamples. %B The Electronic Journal of Combinatorics %V 19 %8 2012/04/16 %G eng %U http://www.combinatorics.org/ojs/index.php/eljc/article/view/2211 %N 2 %0 Journal Article %D 2012 %T Photonic quantum simulation of ground state configurations of Heisenberg square and checkerboard lattice spin systems %A Xiao-song Ma %A Borivoje Dakic %A Sebastian Kropatsche %A William Naylor %A Yang-hao Chan %A Zhe-Xuan Gong %A Lu-ming Duan %A Anton Zeilinger %A Philip Walther %X Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. The available photonic quantum technology is reaching the state where significant advantages arise for the quantum simulation of interesting questions in Heisenberg spin systems. Here we experimentally simulate such spin systems with single photons and linear optics. The effective Heisenberg-type interactions among individual single photons are realized by quantum interference at the tunable direction coupler followed by the measurement process. The effective interactions are characterized by comparing the entanglement dynamics using pairwise concurrence of a four-photon quantum system. We further show that photonic quantum simulations of generalized Heisenberg interactions on a four-site square lattice and a six-site checkerboard lattice are in reach of current technology. %8 2012/05/12 %G eng %U http://arxiv.org/abs/1205.2801v1 %0 Journal Article %J Physical Review E %D 2012 %T Polymer-mediated entropic forces between scale-free objects %A Mohammad F. Maghrebi %A Yacov Kantor %A Mehran Kardar %X The number of configurations of a polymer is reduced in the presence of a barrier or an obstacle. The resulting loss of entropy adds a repulsive component to other forces generated by interaction potentials. When the obstructions are scale invariant shapes (such as cones, wedges, lines or planes) the only relevant length scales are the polymer size R_0 and characteristic separations, severely constraining the functional form of entropic forces. Specifically, we consider a polymer (single strand or star) attached to the tip of a cone, at a separation h from a surface (or another cone). At close proximity, such that h<The Turaev-Viro invariants are scalar topological invariants of three-dimensional manifolds. Here we show that the problem of estimating the Fibonacci version of the Turaev-Viro invariant of a mapping torus is a complete problem for the one clean qubit complexity class (DQC1). This complements a previous result showing that estimating the Turaev-Viro invariant for arbitrary manifolds presented as Heegaard splittings is a complete problem for the standard quantum computation model (BQP). We also discuss a beautiful analogy between these results and previously known results on the computational complexity of approximating the Jones polynomial.

%B In Proceedings of the Sixth Conference on Theory of Quantum Computation, Communication and Cryptography (TQC11) %8 2011/05/31 %G eng %U http://arxiv.org/abs/1105.5100 %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2011 %T Casimir force between sharp-shaped conductors %A Mohammad F. Maghrebi %A Sahand Jamal Rahi %A Thorsten Emig %A Noah Graham %A Robert L. Jaffe %A Mehran Kardar %X Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest. %B Proceedings of the National Academy of Sciences %V 108 %P 6867 - 6871 %8 2011/04/11 %G eng %U http://arxiv.org/abs/1010.3223v1 %N 17 %! Proceedings of the National Academy of Sciences %R 10.1073/pnas.1018079108 %0 Journal Article %J Physical Review A %D 2011 %T Chern numbers hiding in time-of-flight images %A Erhai Zhao %A Noah Bray-Ali %A Carl J. Williams %A I. B. Spielman %A Indubala I. Satija %X We present a technique for detecting topological invariants -- Chern numbers -- from time-of-flight images of ultra-cold atoms. We show that the Chern numbers of integer quantum Hall states of lattice fermions leave their fingerprints in the atoms' momentum distribution. We analytically demonstrate that the number of local maxima in the momentum distribution is equal to the Chern number in two limiting cases, for large hopping anisotropy and in the continuum limit. In addition, our numerical simulations beyond these two limits show that these local maxima persist for a range of parameters. Thus, an everyday observable in cold atom experiments can serve as a useful tool to characterize and visualize quantum states with non-trivial topology. %B Physical Review A %V 84 %8 2011/12/21 %G eng %U http://arxiv.org/abs/1105.3100v3 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.84.063629 %0 Journal Article %D 2011 %T Comment on "Foundation of Statistical Mechanics under Experimentally Realistic Conditions" %A Zhe-Xuan Gong %A L. -M. Duan %X Reimann [Phys. Rev. Lett. 101, 190403 (2008)] claimed that generic isolated macroscopic quantum system will equilibrate under experimentally realistic conditions by proving a theorem. We here show that the proof is invalid for most many-body systems and is unable to demonstrate equilibration in realistic experiment. %8 2011/09/22 %G eng %U http://arxiv.org/abs/1109.4696v1 %0 Journal Article %D 2011 %T Continuous-variable quantum compressed sensing %A Matthias Ohliger %A Vincent Nesme %A David Gross %A Yi-Kai Liu %A Jens Eisert %X We significantly extend recently developed methods to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. Our new method is general enough to allow for measurements from a continuous family, and is also applicable to continuous-variable states. As a technical result, this work generalizes quantum compressed sensing to the situation where the measured observables are taken from a so-called tight frame (rather than an orthonormal basis) --- hence covering most realistic measurement scenarios. As an application, we discuss the reconstruction of quantum states of light from homodyne detection and other types of measurements, and we present simulations that show the advantage of the proposed compressed sensing technique over present methods. Finally, we introduce a method to construct a certificate which guarantees the success of the reconstruction with no assumption on the state, and we show how slightly more measurements give rise to "universal" state reconstruction that is highly robust to noise. %8 2011/11/03 %G eng %U http://arxiv.org/abs/1111.0853v3 %0 Journal Article %J Quantum Information and Computation %D 2011 %T Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States %A Chitambar, Eric %A Carl Miller %A Shi, Yaoyun %K matrix polynomials %K Schwartz-Zippel lemma %K unitary transformations %XIn this brief report, we consider the equivalence between two sets of *m* + 1 bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree m matrix polynomials are unitarily equivalent; i.e. *UA iV*† =

The ground state degeneracy of an $SU(N)_k$ topological phase with $n$ quasiparticle excitations is relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an open question to find a closed formula for this degeneracy for any $N > 2$. Here we present the problem in an explicit combinatorial way and analyze the case N=3. While not finding a complete closed-form solution, we obtain generating functions and solve some special cases.

%8 2010/09/01 %G eng %U http://arxiv.org/abs/1009.0114v1 %0 Journal Article %J Physical Review Letters %D 2010 %T Dynamic Nuclear Polarization in Double Quantum Dots %A Michael Gullans %A J. J. Krich %A J. M. Taylor %A H. Bluhm %A B. I. Halperin %A C. M. Marcus %A M. Stopa %A A. Yacoby %A M. D. Lukin %X We theoretically investigate the controlled dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. Three regimes of long-term dynamics are identified, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. We show that in the case of unequal dots, build up of difference fields generally accompanies the nuclear polarization process, whereas for nearly identical dots, build up of difference fields competes with polarization saturation in dark states. The elimination of the difference field does not, in general, correspond to a stable steady state of the polarization process. %B Physical Review Letters %V 104 %8 2010/6/4 %G eng %U http://arxiv.org/abs/1003.4508v2 %N 22 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.104.226807 %0 Journal Article %D 2010 %T Efficient Direct Tomography for Matrix Product States %A Olivier Landon-Cardinal %A Yi-Kai Liu %A David Poulin %X In this note, we describe a method for reconstructing matrix product states from a small number of efficiently-implementable measurements. Our method is exponentially faster than standard tomography, and it can also be used to certify that the unknown state is an MPS. The basic idea is to use local unitary operations to measure in the Schmidt basis, giving direct access to the MPS representation. This compares favorably with recently and independently proposed methods that recover the MPS tensors by performing a variational minimization, which is computationally intractable in certain cases. Our method also has the advantage of recovering any MPS, while other approaches were limited to special classes of states that exclude important examples such as GHZ and W states. %8 2010/02/24 %G eng %U http://arxiv.org/abs/1002.4632v1 %0 Journal Article %J Nature Communications %D 2010 %T Efficient quantum state tomography %A Marcus Cramer %A Martin B. Plenio %A Steven T. Flammia %A David Gross %A Stephen D. Bartlett %A Rolando Somma %A Olivier Landon-Cardinal %A Yi-Kai Liu %A David Poulin %X Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes infeasible because the number of quantum measurements and the amount of computation required to process them grows exponentially in the system size. Here we show that we can do exponentially better than direct state tomography for a wide range of quantum states, in particular those that are well approximated by a matrix product state ansatz. We present two schemes for tomography in 1-D quantum systems and touch on generalizations. One scheme requires unitary operations on a constant number of subsystems, while the other requires only local measurements together with more elaborate post-processing. Both schemes rely only on a linear number of experimental operations and classical postprocessing that is polynomial in the system size. A further strength of the methods is that the accuracy of the reconstructed states can be rigorously certified without any a priori assumptions. %B Nature Communications %V 1 %P 149 %8 2010/12/21 %G eng %U http://arxiv.org/abs/1101.4366v1 %N 9 %! Nat Comms %R 10.1038/ncomms1147 %0 Journal Article %J Algebra & Number Theory %D 2010 %T An Euler–Poincaré bound for equicharacteristic étale sheaves %A Carl Miller %XThe Grothendieck–Ogg–Shafarevich formula expresses the Euler characteristic of an étale sheaf on a characteristic- curve in terms of local data. The purpose of this paper is to prove an equicharacteristic version of this formula (a bound, rather than an equality). This follows work of R. Pink.

The basis for the proof of this result is the characteristic- Riemann–Hilbert correspondence, which is a functorial relationship between two different types of sheaves on a characteristic- scheme. In the paper we prove a one-dimensional version of this correspondence, considering both local and global settings.

%B Algebra & Number Theory %V 4 %P 21 - 45 %8 2010/01/14 %G eng %U http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.648.3584 %N 1 %! ANT %0 Journal Article %J Nature Phys. %D 2010 %T Far-field optical imaging and manipulation of individual spins with nanoscale resolution %A Maurer, P C %A Maze, J R %A Stanwix, P L %A Jiang, L %A Alexey V. Gorshkov %A Zibrov, A A %A Harke, B %A Hodges, J S %A Zibrov, A S %A Yacoby, A %A Twitchen, D %A Hell, S W %A Walsworth, R L %A Lukin, M D %B Nature Phys. %V 6 %P 912 %G eng %U http://www.nature.com/nphys/journal/v6/n11/abs/nphys1774.html %0 Journal Article %J Physical Review A %D 2010 %T Fast Entanglement Distribution with Atomic Ensembles and Fluorescent Detection %A Jonatan B. Brask %A Liang Jiang %A Alexey V. Gorshkov %A Vladan Vuletic %A Anders S. Sorensen %A Mikhail D. Lukin %X Quantum repeaters based on atomic ensemble quantum memories are promising candidates for achieving scalable distribution of entanglement over long distances. Recently, important experimental progress has been made towards their implementation. However, the entanglement rates and scalability of current approaches are limited by relatively low retrieval and single-photon detector efficiencies. We propose a scheme, which makes use of fluorescent detection of stored excitations to significantly increase the efficiency of connection and hence the rate. Practical performance and possible experimental realizations of the new protocol are discussed. %B Physical Review A %V 81 %8 2010/2/12 %G eng %U http://arxiv.org/abs/0907.3839v2 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.81.020303 %0 Journal Article %J Reviews of Modern Physics %D 2010 %T Feshbach Resonances in Ultracold Gases %A Cheng Chin %A Rudolf Grimm %A Paul Julienne %A Eite Tiesinga %X Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules. %B Reviews of Modern Physics %V 82 %P 1225 - 1286 %8 2010/4/29 %G eng %U http://arxiv.org/abs/0812.1496v2 %N 2 %! Rev. Mod. Phys. %R 10.1103/RevModPhys.82.1225 %0 Journal Article %J Physical Review A %D 2010 %T Heavy fermions in an optical lattice %A Michael Foss-Feig %A Michael Hermele %A Victor Gurarie %A Ana Maria Rey %X We employ a mean-field theory to study ground-state properties and transport of a two-dimensional gas of ultracold alklaline-earth metal atoms governed by the Kondo Lattice Hamiltonian plus a parabolic confining potential. In a homogenous system this mean-field theory is believed to give a qualitatively correct description of heavy fermion metals and Kondo insulators: it reproduces the Kondo-like scaling of the quasiparticle mass in the former, and the same scaling of the excitation gap in the latter. In order to understand ground-state properties in a trap we extend this mean-field theory via local-density approximation. We find that the Kondo insulator gap manifests as a shell structure in the trapped density profile. In addition, a strong signature of the large Fermi surface expected for heavy fermion systems survives the confinement, and could be probed in time-of-flight experiments. From a full self-consistent diagonalization of the mean-field theory we are able to study dynamics in the trap. We find that the mass enhancement of quasiparticle excitations in the heavy Fermi liquid phase manifests as slowing of the dipole oscillations that result from a sudden displacement of the trap center. %B Physical Review A %V 82 %8 2010/11/22 %G eng %U http://arxiv.org/abs/1007.5083v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.82.053624 %0 Journal Article %J Journal of Mathematical Physics %D 2010 %T Matrix pencils and entanglement classification %A Chitambar, Eric %A Carl Miller %A Shi, Yaoyun %XQuantum entanglement plays a central role in quantum information processing. A main objective of the theory is to classify different types of entanglement according to their interconvertibility through manipulations that do not require additional entanglement to perform. While bipartite entanglement is well understood in this framework, the classification of entanglements among three or more subsystems is inherently much more difficult. In this paper, we study pure state entanglement in systems of dimension 2⊗m⊗n. Two states are considered equivalent if they can be reversibly converted from one to the other with a nonzero probability using only local quantum resources and classical communication (SLOCC). We introduce a connection between entanglement manipulations in these systems and the well-studied theory of matrix pencils. All previous attempts to study general SLOCC equivalence in such systems have relied on somewhat contrived techniques which fail to reveal the elegant structure of the problem that can be seen from the matrix pencil approach. Based on this method, we report the first polynomial-time algorithm for deciding when two2⊗m⊗n states are SLOCC equivalent. We then proceed to present a canonical form for all 2⊗m⊗n states based on the matrix pencil construction such that two states are equivalent if and only if they have the same canonical form. Besides recovering the previously known 26 distinct SLOCC equivalence classes in 2⊗3⊗n systems, we also determine the hierarchy between these classes.

%B Journal of Mathematical Physics %V 51 %P 072205 %8 2010/01/01 %G eng %U http://scitation.aip.org/content/aip/journal/jmp/51/7/10.1063/1.3459069 %N 7 %! J. Math. Phys. %R 10.1063/1.3459069 %0 Journal Article %J Physical Review A %D 2010 %T Noise correlations of one-dimensional Bose mixtures in optical lattices %A Anzi Hu %A L. Mathey %A Carl J. Williams %A Charles W. Clark %X We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work, we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity. Here we investigate the signature of these phases in the noise correlations of the atomic cloud after time-of-flight expansion, using both Luttinger liquid theory and the time-evolving block decimation (TEBD) method. We find that paired and counterflow superfluidity exhibit distinctive features in the noise spectra. We treat both extended and inhomogeneous systems, and our numerical work shows that the essential physics of the extended systems is present in the trapped-atom systems of current experimental interest. For paired and counterflow superfluid phases, we suggest methods for extracting Luttinger parameters from noise correlation spectroscopy. %B Physical Review A %V 81 %8 2010/6/2 %G eng %U http://arxiv.org/abs/1002.4918v2 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.81.063602 %0 Journal Article %D 2010 %T Optimal Perfect Distinguishability between Unitaries and Quantum Operations %A Cheng Lu %A Jianxin Chen %A Runyao Duan %X We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula of optimal query time. We extend the sequential condition to general d-dimensional case. Meanwhile, we provide an upper bound and a lower bound for optimal sequential query time. In the process a new iterative method is given, the most notable innovation of which is its independence to auxiliary systems or entanglement. Following the idea, we further obtain an upper bound and a lower bound of (entanglement-assisted) q-maximal fidelities between a unitary and a quantum operation. Thus by the recursion in [1] an upper bound and a lower bound for optimal general perfect discrimination are achieved. Finally our lower bound result can be extended to the case of arbitrary two quantum operations. %8 2010/10/12 %G eng %U http://arxiv.org/abs/1010.2298v1 %0 Journal Article %J Quantum Information & Computation %D 2010 %T Permutational Quantum Computing %A Stephen P. Jordan %XIn topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle trajectory, and computes by permuting particles. Whereas topological quantum computation requires anyons, permutational quantum computation can be performed with ordinary spin-1/2 particles, using a variant of the spin-network scheme of Marzuoli and Rasetti. We do not know whether permutational computation is universal. It may represent a new complexity class within BQP. Nevertheless, permutational quantum computers can in polynomial time approximate matrix elements of certain irreducible representations of the symmetric group and simulate certain processes in the Ponzano-Regge spin foam model of quantum gravity. No polynomial time classical algorithms for these problems are known.

%B Quantum Information & Computation %V 10 %P 470-497 %8 2010/05/01 %G eng %U http://dl.acm.org/citation.cfm?id=2011369 %N 5 %! Quantum Information and Computation Vol. 10 pg. 470 (2010) %0 Journal Article %J Physical Review Letters %D 2010 %T Photonic Phase Gate via an Exchange of Fermionic Spin Waves in a Spin Chain %A Alexey V. Gorshkov %A Johannes Otterbach %A Eugene Demler %A Michael Fleischhauer %A Mikhail D. Lukin %X We propose a new protocol for implementing the two-qubit photonic phase gate. In our approach, the pi phase is acquired by mapping two single photons into atomic excitations with fermionic character and exchanging their positions. The fermionic excitations are realized as spin waves in a spin chain, while photon storage techniques provide the interface between the photons and the spin waves. Possible imperfections and experimental systems suitable for implementing the gate are discussed. %B Physical Review Letters %V 105 %8 2010/8/5 %G eng %U http://arxiv.org/abs/1001.0968v3 %N 6 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.105.060502 %0 Journal Article %D 2010 %T Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians %A Jianxin Chen %A Zhengfeng Ji %A Mary Beth Ruskai %A Bei Zeng %A Duanlu Zhou %X The structure of the ground spaces of quantum systems consisting of local interactions is of fundamental importance to different areas of physics. In this Letter, we present a necessary and sufficient condition for a subspace to be the ground space of a k-local Hamiltonian. Our analysis are motivated by the concept of irreducible correlations studied by [Linden et al., PRL 89, 277906] and [Zhou, PRL 101, 180505], which is in turn based on the principle of maximum entropy. It establishes a better understanding of the ground spaces of local Hamiltonians and builds an intimate link of ground spaces to the correlations of quantum states. %8 2010/10/13 %G eng %U http://arxiv.org/abs/1010.2739v4 %0 Journal Article %J Physical Review A %D 2010 %T Probing the Kondo Lattice Model with Alkaline Earth Atoms %A Michael Foss-Feig %A Michael Hermele %A Ana Maria Rey %X We study transport properties of alkaline-earth atoms governed by the Kondo Lattice Hamiltonian plus a harmonic confining potential, and suggest simple dynamical probes of several different regimes of the phase diagram that can be implemented with current experimental techniques. In particular, we show how Kondo physics at strong coupling, low density, and in the heavy fermion phase is manifest in the dipole oscillations of the conduction band upon displacement of the trap center. %B Physical Review A %V 81 %8 2010/5/7 %G eng %U http://arxiv.org/abs/0912.4762v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.81.051603 %0 Journal Article %D 2010 %T Pseudorandom generators and the BQP vs. PH problem %A Bill Fefferman %A Christopher Umans %X It is a longstanding open problem to devise an oracle relative to which BQP does not lie in the Polynomial-Time Hierarchy (PH). We advance a natural conjecture about the capacity of the Nisan-Wigderson pseudorandom generator [NW94] to fool AC_0, with MAJORITY as its hard function. Our conjecture is essentially that the loss due to the hybrid argument (which is a component of the standard proof from [NW94]) can be avoided in this setting. This is a question that has been asked previously in the pseudorandomness literature [BSW03]. We then make three main contributions: (1) We show that our conjecture implies the existence of an oracle relative to which BQP is not in the PH. This entails giving an explicit construction of unitary matrices, realizable by small quantum circuits, whose row-supports are "nearly-disjoint." (2) We give a simple framework (generalizing the setting of Aaronson [A10]) in which any efficiently quantumly computable unitary gives rise to a distribution that can be distinguished from the uniform distribution by an efficient quantum algorithm. When applied to the unitaries we construct, this framework yields a problem that can be solved quantumly, and which forms the basis for the desired oracle. (3) We prove that Aaronson's "GLN conjecture" [A10] implies our conjecture; our conjecture is thus formally easier to prove. The GLN conjecture was recently proved false for depth greater than 2 [A10a], but it remains open for depth 2. If true, the depth-2 version of either conjecture would imply an oracle relative to which BQP is not in AM, which is itself an outstanding open problem. Taken together, our results have the following interesting interpretation: they give an instantiation of the Nisan-Wigderson generator that can be broken by quantum computers, but not by the relevant modes of classical computation, if our conjecture is true. %8 2010/07/02 %G eng %U http://arxiv.org/abs/1007.0305v3 %0 Journal Article %J Physical Review A %D 2010 %T QMA-complete problems for stoquastic Hamiltonians and Markov matrices %A Stephen P. Jordan %A David Gosset %A Peter J. Love %X We show that finding the lowest eigenvalue of a 3-local symmetric stochastic matrix is QMA-complete. We also show that finding the highest energy of a stoquastic Hamiltonian is QMA-complete and that adiabatic quantum computation using certain excited states of a stoquastic Hamiltonian is universal. We also show that adiabatic evolution in the ground state of a stochastic frustration free Hamiltonian is universal. Our results give a new QMA-complete problem arising in the classical setting of Markov chains, and new adiabatically universal Hamiltonians that arise in many physical systems. %B Physical Review A %V 81 %8 2010/3/29 %G eng %U http://arxiv.org/abs/0905.4755v2 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.81.032331 %0 Journal Article %J Reviews of Modern Physics %D 2010 %T Quantum algorithms for algebraic problems %A Andrew M. Childs %A Wim van Dam %X Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation, and in particular, on problems with an algebraic flavor. %B Reviews of Modern Physics %V 82 %P 1 - 52 %8 2010/1/15 %G eng %U http://arxiv.org/abs/0812.0380v1 %N 1 %! Rev. Mod. Phys. %R 10.1103/RevModPhys.82.1 %0 Journal Article %J Philosophy of Science %D 2010 %T Quantum computation and pseudo-telepathic games %A Jeffrey Bub %X A quantum algorithm succeeds not because the superposition principle allows 'the computation of all values of a function at once' via 'quantum parallelism,' but rather because the structure of a quantum state space allows new sorts of correlations associated with entanglement, with new possibilities for information-processing transformations between correlations, that are not possible in a classical state space. I illustrate this with an elementary example of a problem for which a quantum algorithm is more efficient than any classical algorithm. I also introduce the notion of 'pseudo-telepathic' games and show how the difference between classical and quantum correlations plays a similar role here for games that can be won by quantum players exploiting entanglement, but not by classical players whose only allowed common resource consists of shared strings of random numbers (common causes of the players' correlated responses in a game). %B Philosophy of Science %V 75 %P 458-472 %8 2010/05/14 %G eng %U http://arxiv.org/abs/1005.2449v1 %! Philosophy of Science 75 %0 Journal Article %J Nature %D 2010 %T Quantum Computing %A Thaddeus D. Ladd %A Fedor Jelezko %A Raymond Laflamme %A Yasunobu Nakamura %A Christopher Monroe %A Jeremy L. O'Brien %X Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future. %B Nature %V 464 %P 45 - 53 %8 2010/3/4 %G eng %U http://arxiv.org/abs/1009.2267v1 %N 7285 %! Nature %R 10.1038/nature08812 %0 Journal Article %D 2010 %T Quantum probabilities: an information-theoretic interpretation %A Jeffrey Bub %X This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that \emph{information in the physical sense has new structural features}, just as the transition from classical to relativistic physics rests on the recognition that space-time is structurally different than we thought. Hilbert space, the event space of quantum systems, is interpreted as a kinematic (i.e., pre-dynamic) framework for an indeterministic physics, in the sense that the geometric structure of Hilbert space imposes objective probabilistic or information-theoretic constraints on correlations between events, just as the geometric structure of Minkowski space in special relativity imposes spatio-temporal kinematic constraints on events. The interpretation of quantum probabilities is more subjectivist in spirit than other discussions in this book (e.g., the chapter by Timpson), insofar as the quantum state is interpreted as a credence function---a bookkeeping device for keeping track of probabilities---but it is also objective (or intersubjective), insofar as the credences specified by the quantum state are understood as uniquely determined, via Gleason's theorem, by objective correlational constraints on events in the nonclassical quantum event space defined by the subspace structure of Hilbert space. %8 2010/05/14 %G eng %U http://arxiv.org/abs/1005.2448v1 %0 Journal Article %J Proc. RANDOM %D 2010 %T Quantum property testing for bounded-degree graphs %A Andris Ambainis %A Andrew M. Childs %A Yi-Kai Liu %X We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion, we also prove an Omega(N^(1/4)) quantum query lower bound, thus ruling out the possibility of an exponential quantum speedup. Our quantum algorithms follow from a combination of classical property testing techniques due to Goldreich and Ron, derandomization, and the quantum algorithm for element distinctness. The quantum lower bound is obtained by the polynomial method, using novel algebraic techniques and combinatorial analysis to accommodate the graph structure. %B Proc. RANDOM %P 365-376 %8 2010/12/14 %G eng %U http://arxiv.org/abs/1012.3174v3 %! Proceedings of RANDOM 2011 %R 10.1007/978-3-642-22935-0_31 %0 Journal Article %J Physical Review Letters %D 2010 %T Quantum state tomography via compressed sensing %A David Gross %A Yi-Kai Liu %A Steven T. Flammia %A Stephen Becker %A Jens Eisert %X We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rd log^2 d) measurement settings, compared to standard methods that require d^2 settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low-rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed. We present both theoretical bounds and numerical simulations. %B Physical Review Letters %V 105 %8 2010/10/4 %G eng %U http://arxiv.org/abs/0909.3304v4 %N 15 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.105.150401 %0 Journal Article %J Communications in Mathematical Physics %D 2010 %T On the relationship between continuous- and discrete-time quantum walk %A Andrew M. Childs %X Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations. %B Communications in Mathematical Physics %V 294 %P 581 - 603 %8 2009/10/10 %G eng %U http://arxiv.org/abs/0810.0312v3 %N 2 %! Commun. Math. Phys. %R 10.1007/s00220-009-0930-1 %0 Journal Article %D 2010 %T Simulating sparse Hamiltonians with star decompositions %A Andrew M. Childs %A Robin Kothari %X We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts for time t, this algorithm uses (d^2(d+log* N)||Ht||)^{1+o(1)} queries. This improves the complexity of the sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders, which scales like (d^4(log* N)||Ht||)^{1+o(1)}. To achieve this, we decompose a general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of non-zero entries have the property that every connected component is a star, and efficiently simulate each of these pieces. %8 2010/03/18 %G eng %U http://arxiv.org/abs/1003.3683v2 %! Theory of Quantum Computation %R 10.1007/978-3-642-18073-6_8 %0 Journal Article %J Physical Review Letters %D 2010 %T Temperature driven structural phase transition for trapped ions and its experimental detection %A Zhe-Xuan Gong %A G. -D. Lin %A L. -M. Duan %X A Wigner crystal formed with trapped ion can undergo structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be solely driven by change of the system's temperature. We determine a finite-temperature phase diagram for trapped ions using the renormalization group method and the path integral formalism, and propose an experimental scheme to observe the predicted temperature-driven structural phase transition, which is well within the reach of the current ion trap technology. %B Physical Review Letters %V 105 %8 2010/12/29 %G eng %U http://arxiv.org/abs/1009.0089v1 %N 26 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.105.265703 %0 Journal Article %J Harvard University Physics Department %D 2010 %T Thesis: Novel Systems and Methods for Quantum Communication, Quantum Computation, and Quantum Simulation %A Alexey V. Gorshkov %B Harvard University Physics Department %V Ph.D. Thesis %G eng %0 Journal Article %J Nature Phys. %D 2010 %T Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms %A Alexey V. Gorshkov %A Hermele, M %A Gurarie, V %A Xu, C %A Julienne, P S %A Ye, J %A Zoller, P %A Demler, E %A Lukin, M D %A Rey, A M %B Nature Phys. %V 6 %P 289 %G eng %U http://www.nature.com/nphys/journal/v6/n4/abs/nphys1535.html %0 Journal Article %J Foundations of Physics %D 2010 %T Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal %A Jeffrey Bub %X Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann's 'no hidden variables' proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense 'like Bohm's theory.' His seminal result provides a positive answer to the question. I argue that Bell's analysis misconstrues von Neumann's argument. What von Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the 'beables' of the theory, to use Bell's term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm's theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system. %B Foundations of Physics %V 40 %P 1333 - 1340 %8 2010/6/11 %G eng %U http://arxiv.org/abs/1006.0499v1 %N 9-10 %! Found Phys %R 10.1007/s10701-010-9480-9 %0 Journal Article %J Physical Review Letters %D 2009 %T Alkaline-Earth-Metal Atoms as Few-Qubit Quantum Registers %A Alexey V. Gorshkov %A Ana Maria Rey %A Andrew J. Daley %A Martin M. Boyd %A Jun Ye %A Peter Zoller %A Mikhail D. Lukin %X We propose and analyze a novel approach to quantum information processing, in which multiple qubits can be encoded and manipulated using electronic and nuclear degrees of freedom associated with individual alkaline-earth atoms trapped in an optical lattice. Specifically, we describe how the qubits within each register can be individually manipulated and measured with sub-wavelength optical resolution. We also show how such few-qubit registers can be coupled to each other in optical superlattices via conditional tunneling to form a scalable quantum network. Finally, potential applications to quantum computation and precision measurements are discussed. %B Physical Review Letters %V 102 %8 2009/3/18 %G eng %U http://arxiv.org/abs/0812.3660v2 %N 11 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.102.110503 %0 Journal Article %D 2009 %T Black-box Hamiltonian simulation and unitary implementation %A Dominic W. Berry %A Andrew M. Childs %X We present general methods for simulating black-box Hamiltonians using quantum walks. These techniques have two main applications: simulating sparse Hamiltonians and implementing black-box unitary operations. In particular, we give the best known simulation of sparse Hamiltonians with constant precision. Our method has complexity linear in both the sparseness D (the maximum number of nonzero elements in a column) and the evolution time t, whereas previous methods had complexity scaling as D^4 and were superlinear in t. We also consider the task of implementing an arbitrary unitary operation given a black-box description of its matrix elements. Whereas standard methods for performing an explicitly specified N x N unitary operation use O(N^2) elementary gates, we show that a black-box unitary can be performed with bounded error using O(N^{2/3} (log log N)^{4/3}) queries to its matrix elements. In fact, except for pathological cases, it appears that most unitaries can be performed with only O(sqrt{N}) queries, which is optimal. %8 2009/10/22 %G eng %U http://arxiv.org/abs/0910.4157v4 %! Quantum Information and Computation 12 %0 Journal Article %J Physical Review A %D 2009 %T Collisional cooling of ultra-cold atom ensembles using Feshbach resonances %A L. Mathey %A Eite Tiesinga %A Paul S. Julienne %A Charles W. Clark %X We propose a new type of cooling mechanism for ultra-cold fermionic atom ensembles, which capitalizes on the energy dependence of inelastic collisions in the presence of a Feshbach resonance. We first discuss the case of a single magnetic resonance, and find that the final temperature and the cooling rate is limited by the width of the resonance. A concrete example, based on a p-wave resonance of $^{40}$K, is given. We then improve upon this setup by using both a very sharp optical or radio-frequency induced resonance and a very broad magnetic resonance and show that one can improve upon temperatures reached with current technologies. %B Physical Review A %V 80 %8 2009/9/8 %G eng %U http://arxiv.org/abs/0903.2568v1 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.80.030702 %0 Journal Article %J Foundations of Physics %D 2009 %T Contextuality and nonlocality in 'no signaling' theories %A Jeffrey Bub %A Allen Stairs %X We define a family of 'no signaling' bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The marginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the `no signaling' polytope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum resources for all inputs. We comment on the significance of these results for contextuality and nonlocality in 'no signaling' theories. %B Foundations of Physics %V 39 %P 690 - 711 %8 2009/4/21 %G eng %U http://arxiv.org/abs/0903.1462v2 %N 7 %! Found Phys %R 10.1007/s10701-009-9307-8 %0 Journal Article %J Physical Review A %D 2009 %T Counterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices %A Anzi Hu %A L. Mathey %A Ippei Danshita %A Eite Tiesinga %A Carl J. Williams %A Charles W. Clark %X We study the quantum phases of mixtures of ultra-cold bosonic atoms held in an optical lattice that confines motion or hopping to one spatial dimension. The phases are found by using Tomonaga-Luttinger liquid theory as well as the numerical method of time evolving block decimation (TEBD). We consider a binary mixture with repulsive intra-species interactions, and either repulsive or attractive inter-species interaction. For a homogeneous system, we find paired- and counterflow-superfluid phases at different filling and hopping energies. We also predict parameter regions in which these types of superfluid order coexist with charge density wave order. We show that the Tomonaga-Luttinger liquid theory and TEBD qualitatively agree on the location of the phase boundary to superfluidity. We then describe how these phases are modified and can be detected when an additional harmonic trap is present. In particular, we show how experimentally measurable quantities, such as time-of-flight images and the structure factor, can be used to distinguish the quantum phases. Finally, we suggest applying a Feshbach ramp to detect the paired superfluid state, and a $\pi/2$ pulse followed by Bragg spectroscopy to detect the counterflow superfluid phase. %B Physical Review A %V 80 %8 2009/8/24 %G eng %U http://arxiv.org/abs/0906.2150v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.80.023619 %0 Journal Article %J Theory of Computing %D 2009 %T Discrete-query quantum algorithm for NAND trees %A Andrew M. Childs %A Richard Cleve %A Stephen P. Jordan %A David Yeung %X Recently, Farhi, Goldstone, and Gutmann gave a quantum algorithm for evaluating NAND trees that runs in time O(sqrt(N log N)) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorithm using O(N^{1/2 + epsilon}) queries in the conventional quantum query model, for any fixed epsilon > 0. %B Theory of Computing %V 5 %P 119 - 123 %8 2009/07/01 %G eng %U http://arxiv.org/abs/quant-ph/0702160v1 %N 1 %! Theory of Comput. %R 10.4086/toc.2009.v005a005 %0 Journal Article %J Physical Review A %D 2009 %T Efficient quantum circuits for arbitrary sparse unitaries %A Stephen P. Jordan %A Pawel Wocjan %X Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row or column, and these entries are efficiently computable. One can formulate a model of computation based on the composition of sparse unitaries which includes the quantum Turing machine model, the quantum circuit model, anyonic models, permutational quantum computation, and discrete time quantum walks as special cases. Thus we obtain a simple unified proof that these models are all contained in BQP. Furthermore our general method for implementing sparse unitaries simplifies several existing quantum algorithms. %B Physical Review A %V 80 %8 2009/12/1 %G eng %U http://arxiv.org/abs/0904.2211v2 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.80.062301 %0 Journal Article %D 2009 %T Efficient quantum processing of ideals in finite rings %A Pawel M. Wocjan %A Stephen P. Jordan %A Hamed Ahmadi %A Joseph P. Brennan %X Suppose we are given black-box access to a finite ring R, and a list of generators for an ideal I in R. We show how to find an additive basis representation for I in poly(log |R|) time. This generalizes a recent quantum algorithm of Arvind et al. which finds a basis representation for R itself. We then show that our algorithm is a useful primitive allowing quantum computers to rapidly solve a wide variety of problems regarding finite rings. In particular we show how to test whether two ideals are identical, find their intersection, find their quotient, prove whether a given ring element belongs to a given ideal, prove whether a given element is a unit, and if so find its inverse, find the additive and multiplicative identities, compute the order of an ideal, solve linear equations over rings, decide whether an ideal is maximal, find annihilators, and test the injectivity and surjectivity of ring homomorphisms. These problems appear to be hard classically. %8 2009/07/31 %G eng %U http://arxiv.org/abs/0908.0022v1 %0 Journal Article %J Physical Review A %D 2009 %T Entanglement Cost of Nonlocal Measurements %A Somshubhro Bandyopadhyay %A Gilles Brassard %A Shelby Kimmel %A William K. Wootters %X For certain joint measurements on a pair of spatially separated particles, we ask how much entanglement is needed to carry out the measurement exactly. For a class of orthogonal measurements on two qubits with partially entangled eigenstates, we present upper and lower bounds on the entanglement cost. The upper bound is based on a recent result by D. Berry [Phys. Rev. A 75, 032349 (2007)]. The lower bound, based on the entanglement production capacity of the measurement, implies that for almost all measurements in the class we consider, the entanglement required to perform the measurement is strictly greater than the average entanglement of its eigenstates. On the other hand, we show that for any complete measurement in d x d dimensions that is invariant under all local Pauli operations, the cost of the measurement is exactly equal to the average entanglement of the states associated with the outcomes. %B Physical Review A %V 80 %8 2009/7/15 %G eng %U http://arxiv.org/abs/0809.2264v4 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.80.012313 %0 Journal Article %J Quantum Information and Computation %D 2009 %T Estimating Jones and HOMFLY polynomials with One Clean Qubit %A Stephen P. Jordan %A Pawel Wocjan %XThe Jones and HOMFLY polynomials are link invariants with close connections to quantum computing. It was recently shown that finding a certain approximation to the Jones polynomial of the trace closure of a braid at the fifth root of unity is a complete problem for the one clean qubit complexity class. This is the class of problems solvable in polynomial time on a quantum computer acting on an initial state in which one qubit is pure and the rest are maximally mixed. Here we generalize this result by showing that one clean qubit computers can efficiently approximate the Jones and single-variable HOMFLY polynomials of the trace closure of a braid at any root of unity.

%B Quantum Information and Computation %V 9 %P 264-289 %8 2009/03/01 %G eng %U http://dl.acm.org/citation.cfm?id=2011787 %N 3 %0 Journal Article %J EPL (Europhysics Letters) %D 2009 %T Geometric-Phase-Effect Tunnel-Splitting Oscillations in Single-Molecule Magnets with Fourth-Order Anisotropy Induced by Orthorhombic Distortion %A Michael Foss-Feig %A Jonathan R. Friedman %X We analyze the interference between tunneling paths that occurs for a spin system with both fourth-order and second-order transverse anisotropy. Using an instanton approach, we find that as the strength of the second-order transverse anisotropy is increased, the tunnel splitting is modulated, with zeros occurring periodically. This effect results from the interference of four tunneling paths connecting easy-axis spin orientations and occurs in the absence of any magnetic field. %B EPL (Europhysics Letters) %V 86 %P 27002 %8 2009/04/30 %G eng %U http://arxiv.org/abs/0809.2289v2 %N 2 %! Europhys. Lett. %R 10.1209/0295-5075/86/27002 %0 Journal Article %D 2009 %T Limitations on the simulation of non-sparse Hamiltonians %A Andrew M. Childs %A Robin Kothari %X The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a no--fast-forwarding theorem. Here, we consider non-sparse Hamiltonians and show significant limitations on their simulation. We generalize the no--fast-forwarding theorem to dense Hamiltonians, ruling out generic simulations taking time o(||Ht||), even though ||H|| is not a unique measure of the size of a dense Hamiltonian $H$. We also present a stronger limitation ruling out the possibility of generic simulations taking time poly(||Ht||,log N), showing that known simulations based on discrete-time quantum walk cannot be dramatically improved in general. On the positive side, we show that some non-sparse Hamiltonians can be simulated efficiently, such as those with graphs of small arboricity. %8 2009/08/31 %G eng %U http://arxiv.org/abs/0908.4398v2 %! Quantum Information and Computation 10 %0 Journal Article %J Quantum Information and Computation %D 2009 %T Locality Bounds on Hamiltonians for Stabilizer Codes %A Stephen S. Bullock %A Dianne P. O'Leary %X In this paper, we study the complexity of Hamiltonians whose groundstate is a stabilizer code. We introduce various notions of k-locality of a stabilizer code, inherited from the associated stabilizer group. A choice of generators leads to a Hamiltonian with the code in its groundspace. We establish bounds on the locality of any other Hamiltonian whose groundspace contains such a code, whether or not its Pauli tensor summands commute. Our results provide insight into the cost of creating an energy gap for passive error correction and for adiabatic quantum computing. The results simplify in the cases of XZ-split codes such as Calderbank-Shor-Steane stabilizer codes and topologically-ordered stabilizer codes arising from surface cellulations. %B Quantum Information and Computation %V 9 %8 2009/09/22 %G eng %U http://www.cs.umd.edu/~oleary/reprints/j91.pdf %0 Journal Article %J Phys. Rev. Lett. %D 2009 %T Many-Body Treatment of the Collisional Frequency Shift in Fermionic Atoms %A Rey, A M %A Alexey V. Gorshkov %A Rubbo, C %B Phys. Rev. Lett. %V 103 %P 260402 %G eng %U http://link.aps.org/abstract/PRL/v103/e260402/ %0 Journal Article %J New Journal of Physics %D 2009 %T Multi-channel modelling of the formation of vibrationally cold polar KRb molecules %A Svetlana Kotochigova %A Eite Tiesinga %A Paul S. Julienne %X We describe the theoretical advances that influenced the experimental creation of vibrationally and translationally cold polar $^{40}$K$^{87}$Rb molecules \cite{nphys08,science08}. Cold molecules were created from very-weakly bound molecules formed by magnetic field sweeps near a Feshbach resonance in collisions of ultra-cold $^{40}$K and $^{87}$Rb atoms. Our analysis include the multi-channel bound-state calculations of the hyperfine and Zeeman mixed X$^1\Sigma^+$ and a$^3\Sigma^+$ vibrational levels. We find excellent agreement with the hyperfine structure observed in experimental data. In addition, we studied the spin-orbit mixing in the intermediate state of the Raman transition. This allowed us to investigate its effect on the vibrationally-averaged transition dipole moment to the lowest ro-vibrational level of the X$^1\Sigma^+$ state. Finally, we obtained an estimate of the polarizability of the initial and final ro-vibrational states of the Raman transition near frequencies relevant for optical trapping of the molecules. %B New Journal of Physics %V 11 %P 055043 %8 2009/05/14 %G eng %U http://arxiv.org/abs/0901.1486v1 %N 5 %! New J. Phys. %R 10.1088/1367-2630/11/5/055043 %0 Journal Article %J Physical Review Letters %D 2009 %T Number Fluctuations and Energy Dissipation in Sodium Spinor Condensates %A Yingmei Liu %A Eduardo Gomez %A Stephen E. Maxwell %A Lincoln D. Turner %A Eite Tiesinga %A Paul D. Lett %X We characterize fluctuations in atom number and spin populations in F=1 sodium spinor condensates. We find that the fluctuations enable a quantitative measure of energy dissipation in the condensate. The time evolution of the population fluctuations shows a maximum. We interpret this as evidence of a dissipation-driven separatrix crossing in phase space. For a given initial state, the critical time to the separatrix crossing is found to depend exponentially on the magnetic field and linearly on condensate density. This crossing is confirmed by tracking the energy of the spinor condensate as well as by Faraday rotation spectroscopy. We also introduce a phenomenological model that describes the observed dissipation with a single coefficient. %B Physical Review Letters %V 102 %8 2009/6/5 %G eng %U http://arxiv.org/abs/0906.2110v1 %N 22 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.102.225301 %0 Journal Article %J Physical Review A %D 2009 %T Prediction of Feshbach resonances from three input parameters %A Thomas M. Hanna %A Eite Tiesinga %A Paul S. Julienne %X We have developed a model of Feshbach resonances in gases of ultracold alkali metal atoms using the ideas of multichannel quantum defect theory. Our model requires just three parameters describing the interactions - the singlet and triplet scattering lengths, and the long range van der Waals coefficient - in addition to known atomic properties. Without using any further details of the interactions, our approach can accurately predict the locations of resonances. It can also be used to find the singlet and triplet scattering lengths from measured resonance data. We apply our technique to $^{6}$Li--$^{40}$K and $^{40}$K--$^{87}$Rb scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique. %B Physical Review A %V 79 %8 2009/4/30 %G eng %U http://arxiv.org/abs/0903.0884v2 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.79.040701 %0 Journal Article %J Physical Review A %D 2009 %T Protocol for Hybrid Entanglement Between a Trapped Atom and a Semiconductor Quantum Dot %A Edo Waks %A Christopher Monroe %X We propose a quantum optical interface between an atomic and solid state system. We show that quantum states in a single trapped atom can be entangled with the states of a semiconductor quantum dot through their common interaction with a classical laser field. The interference and detection of the resulting scattered photons can then herald the entanglement of the disparate atomic and solid-state quantum bits. We develop a protocol that can succeed despite a significant mismatch in the radiative characteristics of the two matter-based qubits. We study in detail a particular case of this interface applied to a single trapped \Yb ion and a cavity-coupled InGaAs semiconductor quantum dot. Entanglement fidelity and success rates are found to be robust to a broad range of experimental nonideal effects such as dispersion mismatch, atom recoil, and multi-photon scattering. We conclude that it should be possible to produce highly entangled states of these complementary qubit systems under realistic experimental conditions. %B Physical Review A %V 80 %8 2009/12/30 %G eng %U http://arxiv.org/abs/0907.0444v1 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.80.062330 %0 Journal Article %J Physical Review A %D 2009 %T Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing %A Michael J. O'Hara %A Dianne P. O'Leary %X Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but useful for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians. We then prove that adiabatic quantum computing can realize the ground states of Hamiltonians with certain random interactions, as well as the ground states of one, two, and three-dimensional fermionic interaction lattices, in polynomial time. Finally, we use the Jordan-Wigner transformation and a related transformation for spin-3/2 particles to show that our results can be restated using spin operators in a surprisingly simple manner. A direct consequence is that the one-dimensional cluster state can be found in polynomial time using adiabatic quantum computing. %B Physical Review A %V 79 %8 2009/3/24 %G eng %U http://arxiv.org/abs/0808.1768v1 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.79.032331 %0 Journal Article %J Proc. ACM Symposium on Theory of Computing (STOC) %D 2009 %T Quantum Algorithms Using the Curvelet Transform %A Yi-Kai Liu %X The curvelet transform is a directional wavelet transform over R^n, which is used to analyze functions that have singularities along smooth surfaces (Candes and Donoho, 2002). I demonstrate how this can lead to new quantum algorithms. I give an efficient implementation of a quantum curvelet transform, together with two applications: a single-shot measurement procedure for approximately finding the center of a ball in R^n, given a quantum-sample over the ball; and, a quantum algorithm for finding the center of a radial function over R^n, given oracle access to the function. I conjecture that these algorithms succeed with constant probability, using one quantum-sample and O(1) oracle queries, respectively, independent of the dimension n -- this can be interpreted as a quantum speed-up. To support this conjecture, I prove rigorous bounds on the distribution of probability mass for the continuous curvelet transform. This shows that the above algorithms work in an idealized "continuous" model. %B Proc. ACM Symposium on Theory of Computing (STOC) %P 391-400 %8 2009/10/28 %G eng %U http://arxiv.org/abs/0810.4968v2 %! Proc. ACM Symposium on Theory of Computing (STOC) %0 Journal Article %J Physical Review Letters %D 2009 %T Quantum Phase Transitions and Continuous Observation of Spinor Dynamics in an Antiferromagnetic Condensate %A Yingmei Liu %A Sebastian Jung %A Stephen E. Maxwell %A Lincoln D. Turner %A Eite Tiesinga %A Paul. D. Lett %X Condensates of spin-1 sodium display rich spin dynamics due to the antiferromagnetic nature of the interactions in this system. We use Faraday rotation spectroscopy to make a continuous and minimally destructive measurement of the dynamics over multiple spin oscillations on a single evolving condensate. This method provides a sharp signature to locate a magnetically tuned separatrix in phase space which depends on the net magnetization. We also observe a phase transition from a two- to a three-component condensate at a low but finite temperature using a Stern-Gerlach imaging technique. This transition should be preserved as a zero-temperature quantum phase transition. %B Physical Review Letters %V 102 %8 2009/3/23 %G eng %U http://arxiv.org/abs/0902.3189v1 %N 12 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.102.125301 %0 Journal Article %D 2009 %T The quantum query complexity of certification %A Andris Ambainis %A Andrew M. Childs %A François Le Gall %A Seiichiro Tani %X We study the quantum query complexity of finding a certificate for a d-regular, k-level balanced NAND formula. Up to logarithmic factors, we show that the query complexity is Theta(d^{(k+1)/2}) for 0-certificates, and Theta(d^{k/2}) for 1-certificates. In particular, this shows that the zero-error quantum query complexity of evaluating such formulas is O(d^{(k+1)/2}) (again neglecting a logarithmic factor). Our lower bound relies on the fact that the quantum adversary method obeys a direct sum theorem. %8 2009/03/06 %G eng %U http://arxiv.org/abs/0903.1291v2 %! Quantum Information and Computation 10 %0 Journal Article %J Physical Review A %D 2009 %T Realization of Coherent Optically Dense Media via Buffer-Gas Cooling %A Tao Hong %A Alexey V. Gorshkov %A David Patterson %A Alexander S. Zibrov %A John M. Doyle %A Mikhail D. Lukin %A Mara G. Prentiss %X We demonstrate that buffer-gas cooling combined with laser ablation can be used to create coherent optical media with high optical depth and low Doppler broadening that offers metastable states with low collisional and motional decoherence. Demonstration of this generic technique opens pathways to coherent optics with a large variety of atoms and molecules. We use helium buffer gas to cool 87Rb atoms to below 7 K and slow atom diffusion to the walls. Electromagnetically induced transparency (EIT) in this medium allows for 50% transmission in a medium with initial OD >70 and for slow pulse propagation with large delay-bandwidth products. In the high-OD regime, we observe high-contrast spectrum oscillations due to efficient four-wave mixing. %B Physical Review A %V 79 %8 2009/1/6 %G eng %U http://arxiv.org/abs/0805.1416v2 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.79.013806 %0 Journal Article %J J. Mod. Opt. %D 2009 %T Slow light propagation and amplification via electromagnetically induced transparency and four-wave mixing in an optically dense atomic vapor %A Phillips, N B %A Alexey V. Gorshkov %A Novikova, I %B J. Mod. Opt. %V 56 %P 1916 %G eng %U http://www.informaworld.com/smpp/content db=all content=a913545405 %0 Journal Article %J Physical Review Letters %D 2009 %T Universal computation by quantum walk %A Andrew M. Childs %X In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is restricted to be a sparse matrix with all entries equal to 0 or 1, i.e., the adjacency matrix of a low-degree graph. Thus quantum walk can be regarded as a universal computational primitive, with any desired quantum computation encoded entirely in some underlying graph. The main idea of the construction is to implement quantum gates by scattering processes. %B Physical Review Letters %V 102 %8 2009/5/4 %G eng %U http://arxiv.org/abs/0806.1972v1 %N 18 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.102.180501 %0 Journal Article %J Physical Review A %D 2008 %T The adiabatic theorem in the presence of noise %A Michael J. O'Hara %A Dianne P. O'Leary %X We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian, coupling to low-energy quantum systems, and decoherent time-dependent perturbations in the Hamiltonian. For decoherent perturbations, we find both upper and lower bounds on the evolution time to guarantee the adiabatic approximation performs within a prescribed tolerance. Our new results include explicit definitions of constants, and we apply them to the spin-1/2 particle in a rotating magnetic field, and to the superconducting flux qubit. We compare the theoretical bounds on the superconducting flux qubit to simulation results. %B Physical Review A %V 77 %8 2008/4/22 %G eng %U http://arxiv.org/abs/0801.3872v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.77.042319 %0 Journal Article %D 2008 %T Ancilla-Assisted Discrimination of Quantum Gates %A Jianxin Chen %A Mingsheng Ying %X The intrinsic idea of superdense coding is to find as many gates as possible such that they can be perfectly discriminated. In this paper, we consider a new scheme of discrimination of quantum gates, called ancilla-assisted discrimination, in which a set of quantum gates on a $d-$dimensional system are perfectly discriminated with assistance from an $r-$dimensional ancilla system. The main contribution of the present paper is two-fold: (1) The number of quantum gates that can be discriminated in this scheme is evaluated. We prove that any $rd+1$ quantum gates cannot be perfectly discriminated with assistance from the ancilla, and there exist $rd$ quantum gates which can be perfectly discriminated with assistance from the ancilla. (2) The dimensionality of the minimal ancilla system is estimated. We prove that there exists a constant positive number $c$ such that for any $k\leq cr$ quantum gates, if they are $d$-assisted discriminable, then they are also $r$-assisted discriminable, and there are $c^{\prime}r\textrm{}(c^{\prime}>c)$ different quantum gates which can be discriminated with a $d-$dimensional ancilla, but they cannot be discriminated if the ancilla is reduced to an $r-$dimensional system. Thus, the order $O(r)$ of the number of quantum gates that can be discriminated with assistance from an $r-$dimensional ancilla is optimal. The results reported in this paper represent a preliminary step toward understanding the role ancilla system plays in discrimination of quantum gates as well as the power and limit of superdense coding. %8 2008/09/02 %G eng %U http://arxiv.org/abs/0809.0336v1 %0 Journal Article %J Nature Physics %D 2008 %T Anyonic interferometry and protected memories in atomic spin lattices %A Liang Jiang %A Gavin K. Brennen %A Alexey V. Gorshkov %A Klemens Hammerer %A Mohammad Hafezi %A Eugene Demler %A Mikhail D. Lukin %A Peter Zoller %X Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and have been proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, anyons have never been observed in nature directly. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by performing global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations. %B Nature Physics %V 4 %P 482 - 488 %8 2008/4/20 %G eng %U http://arxiv.org/abs/0711.1365v1 %N 6 %! Nat Phys %R 10.1038/nphys943 %0 Journal Article %J Physical Review A %D 2008 %T Avoided crossings between bound states of ultracold Cesium dimers %A Jeremy M. Hutson %A Eite Tiesinga %A Paul S. Julienne %X We present an efficient new computational method for calculating the binding energies of the bound states of ultracold alkali-metal dimers in the presence of magnetic fields. The method is based on propagation of coupled differential equations and does not use a basis set for the interatomic distance coordinate. It is much more efficient than the previous method based on a radial basis set and allows many more spin channels to be included. This is particularly important in the vicinity of avoided crossings between bound states. We characterize a number of different avoided crossings in Cs_2 and compare our converged calculations with experimental results. Small but significant discrepancies are observed in both crossing strengths and level positions, especially for levels with l symmetry (rotational angular momentum L=8). The discrepancies should allow the development of improved potential models in the future. %B Physical Review A %V 78 %8 2008/11/5 %G eng %U http://arxiv.org/abs/0806.2583v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.78.052703 %0 Journal Article %J Physical Review Letters %D 2008 %T Coherence of an optically illuminated single nuclear spin qubit %A Liang Jiang %A M. V. Gurudev Dutt %A Emre Togan %A Lily Childress %A Paola Cappellaro %A J. M. Taylor %A Mikhail D. Lukin %X We investigate the coherence properties of individual nuclear spin quantum bits in diamond [Dutt et al., Science, 316, 1312 (2007)] when a proximal electronic spin associated with a nitrogen-vacancy (NV) center is being interrogated by optical radiation. The resulting nuclear spin dynamics are governed by time-dependent hyperfine interaction associated with rapid electronic transitions, which can be described by a spin-fluctuator model. We show that due to a process analogous to motional averaging in nuclear magnetic resonance, the nuclear spin coherence can be preserved after a large number of optical excitation cycles. Our theoretical analysis is in good agreement with experimental results. It indicates a novel approach that could potentially isolate the nuclear spin system completely from the electronic environment. %B Physical Review Letters %V 100 %8 2008/2/19 %G eng %U http://arxiv.org/abs/0707.1341v2 %N 7 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.100.073001 %0 Journal Article %J Physical Review Letters %D 2008 %T Coherent Quantum Optical Control with Subwavelength Resolution %A Alexey V. Gorshkov %A Liang Jiang %A Markus Greiner %A Peter Zoller %A Mikhail D. Lukin %X We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation and can, in principle, approach a few nanometers. The selectivity is enabled by the nonlinear atomic response, under the conditions of Electromagnetically Induced Transparency, to a control beam with intensity vanishing at a certain location. Practical performance of this technique and its potential applications to quantum information science with cold atoms, ions, and solid-state qubits are discussed. %B Physical Review Letters %V 100 %8 2008/3/7 %G eng %U http://arxiv.org/abs/0706.3879v2 %N 9 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.100.093005 %0 Journal Article %J International Journal of Theoretical Physics %D 2008 %T Efficient scheme for one-way quantum computing in thermal cavities %A Wen-Xing Yang %A Zhe-Xuan Gong %X We propose a practical scheme for one-way quantum computing based on efficient generation of 2D cluster state in thermal cavities. We achieve a controlled-phase gate that is neither sensitive to cavity decay nor to thermal field by adding a strong classical field to the two-level atoms. We show that a 2D cluster state can be generated directly by making every two atoms collide in an array of cavities, with numerically calculated parameters and appropriate operation sequence that can be easily achieved in practical Cavity QED experiments. Based on a generated cluster state in Box$^{(4)}$ configuration, we then implement Grover's search algorithm for four database elements in a very simple way as an example of one-way quantum computing. %B International Journal of Theoretical Physics %V 47 %P 2997 - 3004 %8 2008/4/12 %G eng %U http://arxiv.org/abs/0704.2297v1 %N 11 %! Int J Theor Phys %R 10.1007/s10773-008-9734-x %0 Journal Article %J Quantum Information & Computation %D 2008 %T Estimating Jones polynomials is a complete problem for one clean qubit %A Peter W. Shor %A Stephen P. Jordan %XIt is known that evaluating a certain approximation to the Jones polynomial for the plat closure of a braid is a BQP-complete problem. That is, this problem exactly captures the power of the quantum circuit model. The one clean qubit model is a model of quantum computation in which all but one qubit starts in the maximally mixed state. One clean qubit computers are believed to be strictly weaker than standard quantum computers, but still capable of solving some classically intractable problems. Here we show that evaluating a certain approximation to the Jones polynomial at a fifth root of unity for the trace closure of a braid is a complete problem for the one clean qubit complexity class. That is, a one clean qubit computer can approximate these Jones polynomials in time polynomial in both the number of strands and number of crossings, and the problem of simulating a one clean qubit computer is reducible to approximating the Jones polynomial of the trace closure of a braid.

%B Quantum Information & Computation %V 8 %P 681-714 %8 2008/09/01 %G eng %U http://dl.acm.org/citation.cfm?id=2017011.2017012 %N 8 %0 Journal Article %J Journal of Mathematical Physics %D 2008 %T Existence of Universal Entangler %A Jianxin Chen %A Runyao Duan %A Zhengfeng Ji %A Mingsheng Ying %A Jun Yu %X A gate is called entangler if it transforms some (pure) product states to entangled states. A universal entangler is a gate which transforms all product states to entangled states. In practice, a universal entangler is a very powerful device for generating entanglements, and thus provides important physical resources for accomplishing many tasks in quantum computing and quantum information. This Letter demonstrates that a universal entangler always exists except for a degenerated case. Nevertheless, the problem how to find a universal entangler remains open. %B Journal of Mathematical Physics %V 49 %P 012103 %8 2008/01/01 %G eng %U http://arxiv.org/abs/0704.1473v2 %N 1 %! J. Math. Phys. %R 10.1063/1.2829895 %0 Journal Article %D 2008 %T Fast quantum algorithms for approximating some irreducible representations of groups %A Stephen P. Jordan %X We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this problem. Furthermore, quantum Schur transforms yield efficient solutions for certain irreducible representations of the unitary group. Beyond this, we obtain poly(n)-time quantum algorithms for approximating matrix elements from all the irreducible representations of the alternating group A_n, and all the irreducible representations of polynomial highest weight of U(n), SU(n), and SO(n). These quantum algorithms offer exponential speedup in worst case complexity over the fastest known classical algorithms. On the other hand, we show that average case instances are classically easy, and that the techniques analyzed here do not offer a speedup over classical computation for the estimation of group characters. %8 2008/11/04 %G eng %U http://arxiv.org/abs/0811.0562v2 %0 Journal Article %J Nature Physics %D 2008 %T High-sensitivity diamond magnetometer with nanoscale resolution %A J. M. Taylor %A P. Cappellaro %A L. Childress %A L. Jiang %A D. Budker %A P. R. Hemmer %A A. Yacoby %A R. Walsworth %A M. D. Lukin %X We present a novel approach to the detection of weak magnetic fields that takes advantage of recently developed techniques for the coherent control of solid-state electron spin quantum bits. Specifically, we investigate a magnetic sensor based on Nitrogen-Vacancy centers in room-temperature diamond. We discuss two important applications of this technique: a nanoscale magnetometer that could potentially detect precession of single nuclear spins and an optical magnetic field imager combining spatial resolution ranging from micrometers to millimeters with a sensitivity approaching few femtotesla/Hz$^{1/2}$. %B Nature Physics %V 4 %P 810 - 816 %8 2008/9/14 %G eng %U http://arxiv.org/abs/0805.1367v1 %N 10 %! Nat Phys %R 10.1038/nphys1075 %0 Journal Article %J Physical Review B %D 2008 %T Multilevel effects in the Rabi oscillations of a Josephson phase qubit %A S. K. Dutta %A Frederick W. Strauch %A R. M. Lewis %A Kaushik Mitra %A Hanhee Paik %A T. A. Palomaki %A Eite Tiesinga %A J. R. Anderson %A Alex J. Dragt %A C. J. Lobb %A F. C. Wellstood %X We present Rabi oscillation measurements of a Nb/AlOx/Nb dc superconducting quantum interference device (SQUID) phase qubit with a 100 um^2 area junction acquired over a range of microwave drive power and frequency detuning. Given the slightly anharmonic level structure of the device, several excited states play an important role in the qubit dynamics, particularly at high power. To investigate the effects of these levels, multiphoton Rabi oscillations were monitored by measuring the tunneling escape rate of the device to the voltage state, which is particularly sensitive to excited state population. We compare the observed oscillation frequencies with a simplified model constructed from the full phase qubit Hamiltonian and also compare time-dependent escape rate measurements with a more complete density-matrix simulation. Good quantitative agreement is found between the data and simulations, allowing us to identify a shift in resonance (analogous to the ac Stark effect), a suppression of the Rabi frequency, and leakage to the higher excited states. %B Physical Review B %V 78 %8 2008/9/15 %G eng %U http://arxiv.org/abs/0806.4711v2 %N 10 %! Phys. Rev. B %R 10.1103/PhysRevB.78.104510 %0 Journal Article %J Physical Review A %D 2008 %T Optimal light storage in atomic vapor %A Nathaniel B. Phillips %A Alexey V. Gorshkov %A Irina Novikova %X We study procedures for the optimization of efficiency of light storage and retrieval based on the dynamic form of electromagnetically induced transparency (EIT) in warm Rb vapor. We present a detailed analysis of two recently demonstrated optimization protocols: a time-reversal-based iteration procedure, which finds the optimal input signal pulse shape for any given control field, and a procedure based on the calculation of an optimal control field for any given signal pulse shape. We verify that the two procedures are consistent with each other, and that they both independently achieve the maximum memory efficiency for any given optical depth. We observe good agreement with theoretical predictions for moderate optical depths (<25), while at higher optical depths the experimental efficiency falls below the theoretically predicted values. We identify possible effects responsible for this reduction in memory efficiency. %B Physical Review A %V 78 %8 2008/8/1 %G eng %U http://arxiv.org/abs/0805.3348v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.78.023801 %0 Journal Article %J Physical Review A %D 2008 %T Optimal light storage with full pulse shape control %A Irina Novikova %A Nathaniel B. Phillips %A Alexey V. Gorshkov %X We experimentally demonstrate optimal storage and retrieval of light pulses of arbitrary shape in atomic ensembles. By shaping auxiliary control pulses, we attain efficiencies approaching the fundamental limit and achieve precise retrieval into any predetermined temporal profile. Our techniques, demonstrated in warm Rb vapor, are applicable to a wide range of systems and protocols. As an example, we present their potential application to the creation of optical time-bin qubits and to controlled partial retrieval. %B Physical Review A %V 78 %8 2008/8/20 %G eng %U http://arxiv.org/abs/0805.1927v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.78.021802 %0 Journal Article %J Phys. Rev. A %D 2008 %T Optimal light storage with full pulse-shape control %A Novikova, I %A Phillips, N B %A Alexey V. Gorshkov %B Phys. Rev. A %V 78 %P 021802(R) %G eng %U http://link.aps.org/abstract/PRA/v78/e021802/ %0 Journal Article %J Proc. SPIE %D 2008 %T Optimizing Slow and Stored Light for Multidisciplinary Applications %A Klein, M %A Xiao, Y %A Alexey V. Gorshkov %A M Hohensee %A C D Leung %A M R Browning %A Phillips, D F %A Novikova, I %A Walsworth, R L %B Proc. SPIE %V 6904 %P 69040C %G eng %U http://spie.org/x648.xml?product_id=772216&Search_Origin=QuickSearch&Search_Results_URL=http://spie.org/x1636.xml&Alternate_URL=http://spie.org/x18509.xml&Alternate_URL_Name=timeframe&Alternate_URL_Value=Exhibitors&UseJavascript=1&Please_Wait_URL=http://s %0 Journal Article %J Physical Review A %D 2008 %T Perturbative Gadgets at Arbitrary Orders %A Stephen P. Jordan %A Edward Farhi %X Adiabatic quantum algorithms are often most easily formulated using many-body interactions. However, experimentally available interactions are generally two-body. In 2004, Kempe, Kitaev, and Regev introduced perturbative gadgets, by which arbitrary three-body effective interactions can be obtained using Hamiltonians consisting only of two-body interactions. These three-body effective interactions arise from the third order in perturbation theory. Since their introduction, perturbative gadgets have become a standard tool in the theory of quantum computation. Here we construct generalized gadgets so that one can directly obtain arbitrary k-body effective interactions from two-body Hamiltonians. These effective interactions arise from the kth order in perturbation theory. %B Physical Review A %V 77 %8 2008/6/19 %G eng %U http://arxiv.org/abs/0802.1874v4 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.77.062329 %0 Journal Article %J Physical Review A %D 2008 %T Photon storage in Lambda-type optically dense atomic media. IV. Optimal control using gradient ascent %A Alexey V. Gorshkov %A Tommaso Calarco %A Mikhail D. Lukin %A Anders S. Sorensen %X We use the numerical gradient ascent method from optimal control theory to extend efficient photon storage in Lambda-type media to previously inaccessible regimes and to provide simple intuitive explanations for our optimization techniques. In particular, by using gradient ascent to shape classical control pulses used to mediate photon storage, we open up the possibility of high efficiency photon storage in the non-adiabatic limit, in which analytical solutions to the equations of motion do not exist. This control shaping technique enables an order-of-magnitude increase in the bandwidth of the memory. We also demonstrate that the often discussed connection between time reversal and optimality in photon storage follows naturally from gradient ascent. Finally, we discuss the optimization of controlled reversible inhomogeneous broadening. %B Physical Review A %V 77 %8 2008/4/4 %G eng %U http://arxiv.org/abs/0710.2698v2 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.77.043806 %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2008 %T Polynomial-time quantum algorithm for the simulation of chemical dynamics %A Ivan Kassal %A Stephen P. Jordan %A Peter J. Love %A Masoud Mohseni %A Alán Aspuru-Guzik %X The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and inter-electronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the Born-Oppenheimer approximation, but faster and more efficient as well, for all reactions with more than about four atoms. This is the case even though the entire electronic wavefunction is propagated on a grid with appropriately short timesteps. Although the preparation and measurement of arbitrary states on a quantum computer is inefficient, here we demonstrate how to prepare states of chemical interest efficiently. We also show how to efficiently obtain chemically relevant observables, such as state-to-state transition probabilities and thermal reaction rates. Quantum computers using these techniques could outperform current classical computers with one hundred qubits. %B Proceedings of the National Academy of Sciences %V 105 %P 18681 - 18686 %8 2008/11/24 %G eng %U http://arxiv.org/abs/0801.2986v3 %N 48 %! Proceedings of the National Academy of Sciences %R 10.1073/pnas.0808245105 %0 Journal Article %D 2008 %T The Power of Unentanglement %A Scott Aaronson %A Salman Beigi %A Andrew Drucker %A Bill Fefferman %A Peter Shor %X The class QMA(k), introduced by Kobayashi et al., consists of all languages that can be verified using k unentangled quantum proofs. Many of the simplest questions about this class have remained embarrassingly open: for example, can we give any evidence that k quantum proofs are more powerful than one? Does QMA(k)=QMA(2) for k>=2? Can QMA(k) protocols be amplified to exponentially small error? In this paper, we make progress on all of the above questions. First, we give a protocol by which a verifier can be convinced that a 3SAT formula of size n is satisfiable, with constant soundness, given ~O(sqrt(n)) unentangled quantum witnesses with O(log n) qubits each. Our protocol relies on the existence of very short PCPs. Second, we show that assuming a weak version of the Additivity Conjecture from quantum information theory, any QMA(2) protocol can be amplified to exponentially small error, and QMA(k)=QMA(2) for all k>=2. Third, we prove the nonexistence of "perfect disentanglers" for simulating multiple Merlins with one. %8 2008/04/04 %G eng %U http://arxiv.org/abs/0804.0802v2 %0 Journal Article %J Physical Review B %D 2008 %T Quantum behavior of the dc SQUID phase qubit %A Kaushik Mitra %A F. W. Strauch %A C. J. Lobb %A J. R. Anderson %A F. C. Wellstood %A Eite Tiesinga %X We analyze the behavior of a dc Superconducting Quantum Interference Device (SQUID) phase qubit in which one junction acts as a phase qubit and the rest of the device provides isolation from dissipation and noise in the bias leads. Ignoring dissipation, we find the two-dimensional Hamiltonian of the system and use numerical methods and a cubic approximation to solve Schrodinger's equation for the eigenstates, energy levels, tunneling rates, and expectation value of the currents in the junctions. Using these results, we investigate how well this design provides isolation while preserving the characteristics of a phase qubit. In addition, we show that the expectation value of current flowing through the isolation junction depends on the state of the qubit and can be used for non-destructive read out of the qubit state. %B Physical Review B %V 77 %8 2008/6/13 %G eng %U http://arxiv.org/abs/0805.3680v1 %N 21 %! Phys. Rev. B %R 10.1103/PhysRevB.77.214512 %0