TY - JOUR T1 - Random Pulse Sequences for Qubit Noise Spectroscopy Y1 - 2023 A1 - Kaixin Huang A1 - Demitry Farfurnik A1 - Alireza Seif A1 - Mohammad Hafezi A1 - Yi-Kai Liu AB -
Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for implementing noise spectroscopy are time-consuming, because they require multiple measurements of the noise spectral density at different frequencies. Here we describe an alternative method for quickly characterizing the spectral density. Our method utilizes random pulse sequences, with carefully-controlled correlations among the pulses, to measure arbitrary linear functionals of the noise spectrum. Such measurements allow us to estimate k'th-order moments of the noise spectrum, as well as to reconstruct sparse noise spectra via compressed sensing. Our simulations of the performance of the random pulse sequences on a realistic physical system, self-assembled quantum dots, reveal a speedup of an order of magnitude in extracting the noise spectrum compared to conventional dynamical decoupling approaches.
UR - https://arxiv.org/abs/2303.00909 ER - TY - JOUR T1 - Randomized measurement protocols for lattice gauge theories Y1 - 2023 A1 - Jacob Bringewatt A1 - Jonathan Kunjummen A1 - Niklas Mueller AB -Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum states. While unraveling the intricate structure of quantum states is generally difficult and resource-intensive, quantum systems in nature are often tightly constrained by symmetries. This can be leveraged by the symmetry-conscious randomized measurement schemes we propose, yielding clear advantages over symmetry-blind randomization such as reducing measurement costs, enabling symmetry-based error mitigation in experiments, allowing differentiated measurement of (lattice) gauge theory entanglement structure, and, potentially, the verification of topologically ordered states in existing and near-term experiments.
UR - https://arxiv.org/abs/2303.15519 ER - TY - JOUR T1 - On the Rational Degree of Boolean Functions and Applications Y1 - 2023 A1 - Vishnu Iyer A1 - Siddhartha Jain A1 - Matt Kovacs-Deak A1 - Vinayak M. Kumar A1 - Luke Schaeffer A1 - Daochen Wang A1 - Michael Whitmeyer AB -We study a natural complexity measure of Boolean functions known as the (exact) rational degree. For total functions f, it is conjectured that rdeg(f) is polynomially related to deg(f), where deg(f) is the Fourier degree. Towards this conjecture, we show that symmetric functions have rational degree at least deg(f)/2 and monotone functions have rational degree at least deg(f)−−−−−√. We observe that both of these lower bounds are tight. In addition, we show that all read-once depth-d Boolean formulae have rational degree at least Ω(deg(f)1/d). Furthermore, we show that almost every Boolean function on n variables has rational degree at least n/2−O(n−−√).
In contrast to total functions, we exhibit partial functions that witness unbounded separations between rational and approximate degree, in both directions. As a consequence, we show that for quantum computers, post-selection and bounded-error are incomparable resources in the black-box model.
Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. Despite indications of a wealth of exotic phenomena, the physics of anyons in one dimension (1D) remains largely unexplored. Here, we realize Abelian anyons in 1D with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase via a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks, and observe the anyonic Hanbury Brown-Twiss effect, as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of 1D anyons.
UR - https://arxiv.org/abs/2306.01737 ER - TY - JOUR T1 - Resource theory of quantum uncomplexity JF - Physical Review A Y1 - 2022 A1 - Nicole Yunger Halpern A1 - Naga B. T. Kothakonda A1 - Jonas Haferkamp A1 - Anthony Munson A1 - Jens Eisert A1 - Philippe Faist AB -Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. The greater a state's distance from maximal complexity, or "uncomplexity," the more useful the state is as input to a quantum computation. Separately, resource theories -- simple models for agents subject to constraints -- are burgeoning in quantum information theory. We unite the two domains, confirming Brown and Susskind's conjecture that a resource theory of uncomplexity can be defined. The allowed operations, fuzzy operations, are slightly random implementations of two-qubit gates chosen by an agent. We formalize two operational tasks, uncomplexity extraction and expenditure. Their optimal efficiencies depend on an entropy that we engineer to reflect complexity. We also present two monotones, uncomplexity measures that decline monotonically under fuzzy operations, in certain regimes. This work unleashes on many-body complexity the resource-theory toolkit from quantum information theory.
VL - 106 UR - https://arxiv.org/abs/2110.11371 U5 - 10.1103/physreva.106.062417 ER - TY - JOUR T1 - Rainbow Scars: From Area to Volume Law Y1 - 2021 A1 - Christopher M. Langlett A1 - Zhi-Cheng Yang A1 - Julia Wildeboer A1 - Alexey V. Gorshkov A1 - Thomas Iadecola A1 - Shenglong Xu AB -Quantum many-body scars (QMBS) constitute a new quantum dynamical regime in which rare "scarred" eigenstates mediate weak ergodicity breaking. One open question is to understand the most general setting in which these states arise. In this work, we develop a generic construction that embeds a new class of QMBS, rainbow scars, into the spectrum of an arbitrary Hamiltonian. Unlike other examples of QMBS, rainbow scars display extensive bipartite entanglement entropy while retaining a simple entanglement structure. Specifically, the entanglement scaling is volume-law for a random bipartition, while scaling for a fine-tuned bipartition is sub-extensive. When internal symmetries are present, the construction leads to multiple, and even towers of rainbow scars revealed through distinctive non-thermal dynamics. To this end, we provide an experimental road map for realizing rainbow scar states in a Rydberg-atom quantum simulator, leading to coherent oscillations distinct from the strictly sub-volume-law QMBS previously realized in the same system.
UR - https://arxiv.org/abs/2107.03416 ER - TY - JOUR T1 - Ray-based framework for state identification in quantum dot devices JF - PRX Quantum Y1 - 2021 A1 - Justyna P. Zwolak A1 - Thomas McJunkin A1 - Sandesh S. Kalantre A1 - Samuel F. Neyens A1 - E. R. MacQuarrie A1 - Mark A. Eriksson A1 - J. M. Taylor AB -Quantum dots (QDs) defined with electrostatic gates are a leading platform for a scalable quantum computing implementation. However, with increasing numbers of qubits, the complexity of the control parameter space also grows. Traditional measurement techniques, relying on complete or near-complete exploration via two-parameter scans (images) of the device response, quickly become impractical with increasing numbers of gates. Here, we propose to circumvent this challenge by introducing a measurement technique relying on one-dimensional projections of the device response in the multi-dimensional parameter space. Dubbed as the ray-based classification (RBC) framework, we use this machine learning (ML) approach to implement a classifier for QD states, enabling automated recognition of qubit-relevant parameter regimes. We show that RBC surpasses the 82 % accuracy benchmark from the experimental implementation of image-based classification techniques from prior work while cutting down the number of measurement points needed by up to 70 %. The reduction in measurement cost is a significant gain for time-intensive QD measurements and is a step forward towards the scalability of these devices. We also discuss how the RBC-based optimizer, which tunes the device to a multi-qubit regime, performs when tuning in the two- and three-dimensional parameter spaces defined by plunger and barrier gates that control the dots. This work provides experimental validation of both efficient state identification and optimization with ML techniques for non-traditional measurements in quantum systems with high-dimensional parameter spaces and time-intensive measurements.
VL - 2 UR - https://arxiv.org/abs/2102.11784 CP - 020335 U5 - https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.2.020335 ER - TY - JOUR T1 - Relaxation of non-integrable systems and correlation functions Y1 - 2021 A1 - Riddell, Jonathon A1 - García-Pintos, Luis Pedro A1 - Alhambra, Álvaro M. KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) KW - Statistical Mechanics (cond-mat.stat-mech) KW - Strongly Correlated Electrons (cond-mat.str-el) AB -We investigate early-time equilibration rates of observables in closed many-body quantum systems and compare them to those of two correlation functions, first introduced by Kubo and Srednicki. We explore whether these different rates coincide at a universal value that sets the timescales of processes at a finite energy density. We find evidence for this coincidence when the initial conditions are sufficiently generic, or typical. We quantify this with the effective dimension of the state and with a state-observable effective dimension, which estimate the number of energy levels that participate in the dynamics. Our findings are confirmed by proving that these different timescales coincide for dynamics generated by Haar-random Hamiltonians. This also allows to quantitatively understand the scope of previous theoretical results on equilibration timescales and on random matrix formalisms. We approach this problem with exact, full spectrum diagonalization. The numerics are carried out in a non-integrable Heisenberg-like Hamiltonian, and the dynamics are investigated for several pairs of observables and states.
UR - https://arxiv.org/abs/2112.09475 U5 - 10.48550/ARXIV.2112.09475 ER - TY - JOUR T1 - Resource theory of quantum uncomplexity Y1 - 2021 A1 - Nicole Yunger Halpern A1 - Naga B. T. Kothakonda A1 - Jonas Haferkamp A1 - Anthony Munson A1 - Jens Eisert A1 - Philippe Faist AB -Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. The greater a state's distance from maximal complexity, or ``uncomplexity,'' the more useful the state is as input to a quantum computation. Separately, resource theories -- simple models for agents subject to constraints -- are burgeoning in quantum information theory. We unite the two domains, confirming Brown and Susskind's conjecture that a resource theory of uncomplexity can be defined. The allowed operations, fuzzy operations, are slightly random implementations of two-qubit gates chosen by an agent. We formalize two operational tasks, uncomplexity extraction and expenditure. Their optimal efficiencies depend on an entropy that we engineer to reflect complexity. We also present two monotones, uncomplexity measures that decline monotonically under fuzzy operations, in certain regimes. This work unleashes on many-body complexity the resource-theory toolkit from quantum information theory.
UR - https://arxiv.org/abs/2110.11371 ER - TY - JOUR T1 - Resource-Optimized Fermionic Local-Hamiltonian Simulation on Quantum Computer for Quantum Chemistry JF - Quantum Y1 - 2021 A1 - Qingfeng Wang A1 - Ming Li A1 - Christopher Monroe A1 - Yunseong Nam AB -The ability to simulate a fermionic system on a quantum computer is expected to revolutionize chemical engineering, materials design, nuclear physics, to name a few. Thus, optimizing the simulation circuits is of significance in harnessing the power of quantum computers. Here, we address this problem in two aspects. In the fault-tolerant regime, we optimize the $\rzgate$ and $\tgate$ gate counts along with the ancilla qubit counts required, assuming the use of a product-formula algorithm for implementation. We obtain a savings ratio of two in the gate counts and a savings ratio of eleven in the number of ancilla qubits required over the state of the art. In the pre-fault tolerant regime, we optimize the two-qubit gate counts, assuming the use of the variational quantum eigensolver (VQE) approach. Specific to the latter, we present a framework that enables bootstrapping the VQE progression towards the convergence of the ground-state energy of the fermionic system. This framework, based on perturbation theory, is capable of improving the energy estimate at each cycle of the VQE progression, by about a factor of three closer to the known ground-state energy compared to the standard VQE approach in the test-bed, classically-accessible system of the water molecule. The improved energy estimate in turn results in a commensurate level of savings of quantum resources, such as the number of qubits and quantum gates, required to be within a pre-specified tolerance from the known ground-state energy. We also explore a suite of generalized transformations of fermion to qubit operators and show that resource-requirement savings of up to more than 20% is possible.
VL - 5 UR - https://arxiv.org/abs/2004.04151 CP - 509 U5 - https://doi.org/10.22331/q-2021-07-26-509 ER - TY - JOUR T1 - Robust Self-Testing of Multiparticle Entanglement JF - Phys. Rev. Lett. Y1 - 2021 A1 - Dian Wu A1 - Qi Zhao A1 - Xue-Mei Gu A1 - Han-Sen Zhong A1 - You Zhou A1 - Li-Chao Peng A1 - Jian Qin A1 - Yi-Han Luo A1 - Kai Chen A1 - Li Li A1 - Nai-Le Liu A1 - Chao-Yang Lu A1 - Jian-Wei Pan AB -Quantum self-testing is a device-independent way to certify quantum states and measurements using only the input-output statistics, with minimal assumptions about the quantum devices. Due to the high demand on tolerable noise, however, experimental self-testing was limited to two-photon systems. Here, we demonstrate the first robust self-testing for multi-particle quantum entanglement. We prepare two examples of four-photon graph states, the Greenberger-Horne-Zeilinger (GHZ) states with a fidelity of 0.957(2) and the linear cluster states with a fidelity of 0.945(2). Based on the observed input-output statistics, we certify the genuine four-photon entanglement and further estimate their qualities with respect to realistic noise in a device-independent manner.
VL - 127 U4 - 230503 UR - https://arxiv.org/abs/2105.10298 U5 - https://doi.org/10.1103/PhysRevLett.127.230503 ER - TY - JOUR T1 - RPPLNS: Pay-per-last-N-shares with a Randomised Twist Y1 - 2021 A1 - Philip Lazos A1 - Francisco J. Marmolejo-Cossío A1 - Xinyu Zhou A1 - Jonathan Katz AB -"Pay-per-last-N-shares" (PPLNS) is one of the most common payout strategies used by mining pools in Proof-of-Work (PoW) cryptocurrencies. As with any payment scheme, it is imperative to study issues of incentive compatibility of miners within the pool. For PPLNS this question has only been partially answered; we know that reasonably-sized miners within a PPLNS pool prefer following the pool protocol over employing specific deviations. In this paper, we present a novel modification to PPLNS where we randomise the protocol in a natural way. We call our protocol "Randomised pay-per-last-N-shares" (RPPLNS), and note that the randomised structure of the protocol greatly simplifies the study of its incentive compatibility. We show that RPPLNS maintains the strengths of PPLNS (i.e., fairness, variance reduction, and resistance to pool hopping), while also being robust against a richer class of strategic mining than what has been shown for PPLNS.
UR - https://arxiv.org/abs/2102.07681 ER - TY - JOUR T1 - Random Quantum Batteries JF - Phys. Rev. Research Y1 - 2020 A1 - Francesco Caravelli A1 - Ghislaine Coulter-De Wit A1 - Luis Pedro García-Pintos A1 - Alioscia Hamma AB -Quantum nano-devices are fundamental systems in quantum thermodynamics that have been the subject of profound interest in recent years. Among these, quantum batteries play a very important role. In this paper we lay down a theory of random quantum batteries and provide a systematic way of computing the average work and work fluctuations in such devices by investigating their typical behavior. We show that the performance of random quantum batteries exhibits typicality and depends only on the spectral properties of the time evolving operator, the initial state and the measuring Hamiltonian. At given revival times a random quantum battery features a quantum advantage over classical random batteries. Our method is particularly apt to be used both for exactly solvable models like the Jaynes-Cummings model or in perturbation theory, e.g., systems subject to harmonic perturbations. We also study the setting of quantum adiabatic random batteries.
VL - 2 UR - https://arxiv.org/abs/1908.08064 CP - 023095 U5 - https://doi.org/10.1103/PhysRevResearch.2.023095 ER - TY - JOUR T1 - Raw Image Deblurring Y1 - 2020 A1 - Chih-Hung Liang A1 - Yu-An Chen A1 - Yueh-Cheng Liu A1 - Winston H. Hsu AB -Deep learning-based blind image deblurring plays an essential role in solving image blur since all existing kernels are limited in modeling the real world blur. Thus far, researchers focus on powerful models to handle the deblurring problem and achieve decent results. For this work, in a new aspect, we discover the great opportunity for image enhancement (e.g., deblurring) directly from RAW images and investigate novel neural network structures benefiting RAW-based learning. However, to the best of our knowledge, there is no available RAW image deblurring dataset. Therefore, we built a new dataset containing both RAW images and processed sRGB images and design a new model to utilize the unique characteristics of RAW images. The proposed deblurring model, trained solely from RAW images, achieves the state-of-art performance and outweighs those trained on processed sRGB images. Furthermore, with fine-tuning, the proposed model, trained on our new dataset, can generalize to other sensors. Additionally, by a series of experiments, we demonstrate that existing deblurring models can also be improved by training on the RAW images in our new dataset. Ultimately, we show a new venue for further opportunities based on the devised novel raw-based deblurring method and the brand-new Deblur-RAW dataset.
UR - https://arxiv.org/abs/2012.04264 ER - TY - JOUR T1 - Ray-based classification framework for high-dimensional data JF - Proceedings of the Machine Learning and the Physical Sciences Workshop at NeurIPS 2020, Vancouver, Canada Y1 - 2020 A1 - Justyna P. Zwolak A1 - Sandesh S. Kalantre A1 - Thomas McJunkin A1 - Brian J. Weber A1 - J. M. Taylor AB -While classification of arbitrary structures in high dimensions may require complete quantitative information, for simple geometrical structures, low-dimensional qualitative information about the boundaries defining the structures can suffice. Rather than using dense, multi-dimensional data, we propose a deep neural network (DNN) classification framework that utilizes a minimal collection of one-dimensional representations, called \emph{rays}, to construct the "fingerprint" of the structure(s) based on substantially reduced information. We empirically study this framework using a synthetic dataset of double and triple quantum dot devices and apply it to the classification problem of identifying the device state. We show that the performance of the ray-based classifier is already on par with traditional 2D images for low dimensional systems, while significantly cutting down the data acquisition cost.
UR - https://arxiv.org/abs/2010.00500 ER - TY - JOUR T1 - Realizing and Probing Baryonic Excitations in Rydberg Atom Arrays Y1 - 2020 A1 - Fangli Liu A1 - Seth Whitsitt A1 - Przemyslaw Bienias A1 - Rex Lundgren A1 - Alexey V. Gorshkov AB -We propose a realization of mesonic and baryonic quasiparticle excitations in Rydberg atom arrays with programmable interactions. Recent experiments have shown that such systems possess a Z3-ordered crystalline phase whose low-energy quasiparticles are defects in the crystalline order. By engineering a Z3-translational-symmetry breaking field on top of the Rydberg-blockaded Hamiltonian, we show that different types of defects experience confinement, and as a consequence form mesonic or baryonic quasiparticle excitations. We illustrate the formation of these quasiparticles by studying a quantum chiral clock model related to the Rydberg Hamiltonian. We then propose an experimental protocol involving out-of-equilibrium dynamics to directly probe the spectrum of the confined excitations. We show that the confined quasiparticle spectrum can limit quantum information spreading in this system. This proposal is readily applicable to current Rydberg experiments, and the method can be easily generalized to more complex confined excitations (e.g. `tetraquarks', `pentaquarks') in phases with Zq order for q>3.
UR - https://arxiv.org/abs/2007.07258 ER - TY - JOUR T1 - Resonant enhancement of three-body loss between strongly interacting photons Y1 - 2020 A1 - Marcin Kalinowski A1 - Yidan Wang A1 - Przemyslaw Bienias A1 - Michael Gullans A1 - Dalia P. Ornelas-Huerta A1 - Alexander N. Craddock A1 - Steven L. Rolston A1 - J. V. Porto A1 - Hans Peter Büchler A1 - Alexey V. Gorshkov AB -Rydberg polaritons provide an example of a rare type of system where three-body interactions can be as strong or even stronger than two-body interactions. The three-body interactions can be either dispersive or dissipative, with both types possibly giving rise to exotic, strongly-interacting, and topological phases of matter. Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored. Using a renormalization group technique to solve the three-body Schrödinger equation, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons. We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiment
UR - https://arxiv.org/abs/2010.09772 ER - TY - JOUR T1 - Robust Encoding of a Qubit in a Molecule JF - Phys. Rev. X Y1 - 2020 A1 - Victor V. Albert A1 - Jacob P. Covey A1 - John Preskill AB -We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of rotational states of a rigid body. These codes, which protect against both drift in the body’s orientation and small changes in its angular momentum, may be well suited for robust storage and coherent processing of quantum information using rotational states of a polyatomic molecule. Extensions of such codes to rigid bodies with a symmetry axis are compatible with rotational states of diatomic molecules as well as nuclear states of molecules and atoms. We also describe codes associated with general non-Abelian groups and develop orthogonality relations for coset spaces, laying the groundwork for quantum information processing with exotic configuration spaces.
VL - 10 UR - https://arxiv.org/abs/1911.00099 CP - 031050 U5 - https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.031050 ER - TY - JOUR T1 - Real-time dynamics of string breaking in quantum spin chains Y1 - 2019 A1 - Roberto Verdel A1 - Fangli Liu A1 - Seth Whitsitt A1 - Alexey V. Gorshkov A1 - Markus Heyl AB -String breaking is a central dynamical process in theories featuring confinement, where a string connecting two charges decays at the expense of the creation of new particle-antiparticle pairs. Here, we show that this process can also be observed in quantum Ising chains where domain walls get confined either by a symmetry-breaking field or by long-range interactions. We find that string breaking occurs, in general, as a two-stage process: First, the initial charges remain essentially static and stable. The connecting string, however, can become a dynamical object. We develop an effective description of this motion, which we find is strongly constrained. In the second stage, which can be severely delayed due to these dynamical constraints, the string finally breaks. We observe that the associated time scale can depend crucially on the initial separation between domain walls and can grow by orders of magnitude by changing the distance by just a few lattice sites. We discuss how our results generalize to one-dimensional confining gauge theories and how they can be made accessible in quantum simulator experiments such as Rydberg atoms or trapped ions.
UR - https://arxiv.org/abs/1911.11382 ER - TY - JOUR T1 - Refining the Structure of Neural Networks Using Matrix Conditioning Y1 - 2019 A1 - Roozbeh Yousefzadeh A1 - Dianne P O'Leary AB -Deep learning models have proven to be exceptionally useful in performing many machine learning tasks. However, for each new dataset, choosing an effective size and structure of the model can be a time-consuming process of trial and error. While a small network with few neurons might not be able to capture the intricacies of a given task, having too many neurons can lead to overfitting and poor generalization. Here, we propose a practical method that employs matrix conditioning to automatically design the structure of layers of a feed-forward network, by first adjusting the proportion of neurons among the layers of a network and then scaling the size of network up or down. Results on sample image and non-image datasets demonstrate that our method results in small networks with high accuracies. Finally, guided by matrix conditioning, we provide a method to effectively squeeze models that are already trained. Our techniques reduce the human cost of designing deep learning models and can also reduce training time and the expense of using neural networks for applications.
UR - https://arxiv.org/abs/1908.02400 ER - TY - JOUR T1 - ReQWIRE: Reasoning about Reversible Quantum Circuits JF - EPTCS Y1 - 2019 A1 - Robert Rand A1 - Jennifer Paykin A1 - Dong-Ho Lee A1 - Steve Zdancewic AB -Common 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.
VL - 287 UR - https://arxiv.org/abs/1901.10118 U5 - https://doi.org/10.4204/EPTCS.287.17 ER - TY - JOUR T1 - Resource theory of asymmetric distinguishability for quantum channels Y1 - 2019 A1 - Xin Wang A1 - Mark M. Wilde AB -This 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.
UR - https://arxiv.org/abs/1907.06306 ER - TY - JOUR T1 - Resource theory of entanglement for bipartite quantum channels Y1 - 2019 A1 - Stefan Bäuml A1 - Siddhartha Das A1 - Xin Wang A1 - Mark M. Wilde AB -The 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.
UR - https://arxiv.org/abs/1907.04181 ER - TY - JOUR T1 - Recovering quantum gates from few average gate fidelities JF - Phys. Rev. Lett. Y1 - 2018 A1 - Ingo Roth A1 - Richard Kueng A1 - Shelby Kimmel A1 - Yi-Kai Liu A1 - David Gross A1 - Jens Eisert A1 - Martin Kliesch AB -Characterising 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.
VL - 121 U4 - 170502 UR - https://arxiv.org/abs/1803.00572 U5 - https://doi.org/10.1103/PhysRevLett.121.170502 ER - TY - JOUR T1 - Recovery Map for Fermionic Gaussian Channels Y1 - 2018 A1 - Brian Swingle A1 - Yixu Wang AB -A 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.
UR - https://arxiv.org/abs/1811.04956 ER - TY - JOUR T1 - Resilience of scrambling measurements JF - Phys. Rev. Y1 - 2018 A1 - Brian Swingle A1 - Nicole Yunger Halpern AB -Most 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.
VL - A UR - https://arxiv.org/abs/1802.01587 CP - 97 U5 - https://doi.org/10.1103/PhysRevA.97.062113 ER - TY - JOUR T1 - Resonantly driven CNOT gate for electron spins JF - Science Y1 - 2018 A1 - D. M. Zajac A1 - A. J. Sigillito A1 - M. Russ A1 - F. Borjans A1 - J. M. Taylor A1 - Guido Burkard A1 - J. R. Petta AB -Single-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.
VL - 359 U4 - 439-442 UR - http://science.sciencemag.org/content/359/6374/439 CP - 6374 U5 - 10.1126/science.aao5965 ER - TY - JOUR T1 - Robust two-qubit gates in a linear ion crystal using a frequency-modulated driving force JF - Physical Review Letters Y1 - 2018 A1 - Pak Hong Leung A1 - Kevin A. Landsman A1 - Caroline Figgatt A1 - Norbert M. Linke A1 - Christopher Monroe A1 - Kenneth R. Brown AB -In 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.
VL - 120 U4 - 020501 UR - https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.020501 CP - 2 U5 - 10.1103/PhysRevLett.120.020501 ER - TY - JOUR T1 - Randomness in nonlocal games between mistrustful players JF - Quantum Information and Computation Y1 - 2017 A1 - Carl Miller A1 - Yaoyun Shi AB -If 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.
VL - 17 U4 - 0595-0610 UR - https://arxiv.org/abs/1706.04984 CP - 7&8 ER - TY - JOUR T1 - Raz-McKenzie simulation with the inner product gadget JF - Electronic Colloquium on Computational Complexity (ECCC) Y1 - 2017 A1 - Xiaodi Wu A1 - Penghui Yao A1 - Henry Yuen AB -In 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.
UR - https://eccc.weizmann.ac.il/report/2017/010/ ER - TY - JOUR T1 - On the readiness of quantum optimization machines for industrial applications Y1 - 2017 A1 - Alejandro Perdomo-Ortiz A1 - Alexander Feldman A1 - Asier Ozaeta A1 - Sergei V. Isakov A1 - Zheng Zhu A1 - Bryan O'Gorman A1 - Helmut G. Katzgraber A1 - Alexander Diedrich A1 - Hartmut Neven A1 - Johan de Kleer A1 - Brad Lackey A1 - Rupak Biswas AB -There 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.
UR - https://arxiv.org/abs/1708.09780 ER - TY - JOUR T1 - Rigidity of the magic pentagram game JF - Quantum Science and Technology Y1 - 2017 A1 - Amir Kalev A1 - Carl Miller AB -A 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.
VL - 3 U4 - 015002 UR - http://iopscience.iop.org/article/10.1088/2058-9565/aa931d/meta CP - 1 ER - TY - JOUR T1 - Robust entanglement renormalization on a noisy quantum computer Y1 - 2017 A1 - Isaac H. Kim A1 - Brian Swingle AB -A 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.
UR - https://arxiv.org/abs/1711.07500 ER - TY - JOUR T1 - Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms JF - Physical Review A Y1 - 2016 A1 - Michael E. Beverland A1 - Gorjan Alagic A1 - Michael J. Martin A1 - Andrew P. Koller A1 - Ana M. Rey A1 - Alexey V. Gorshkov AB -We 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.
VL - 93 UR - http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.051601 CP - 5 U5 - 10.1103/PhysRevA.93.051601 ER - TY - JOUR T1 - Robust Protocols for Securely Expanding Randomness and Distributing Keys Using Untrusted Quantum Devices JF - Journal of the ACM Y1 - 2016 A1 - Carl Miller A1 - Yaoyun Shi KW - key distribution KW - nonlocal games KW - privacy KW - quantum cryptography KW - random-number generation KW - untrusted device AB -Randomness 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.
VL - 63 U4 - 33:1–33:63 UR - http://doi.acm.org/10.1145/2885493 CP - 4 U5 - 10.1145/2885493 ER - TY - JOUR T1 - Robust Single-Qubit Process Calibration via Robust Phase Estimation JF - Physical Review A Y1 - 2015 A1 - Shelby Kimmel A1 - Guang Hao Low A1 - Theodore J. Yoder AB - 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)]. VL - 92 U4 - 062315 UR - http://arxiv.org/abs/1502.02677 CP - 6 U5 - 10.1103/PhysRevA.92.062315 ER - TY - JOUR T1 - Remote tomography and entanglement swapping via von Neumann–Arthurs–Kelly interaction JF - Physical Review A Y1 - 2014 A1 - S. M. Roy A1 - Abhinav Deshpande A1 - Nitica Sakharwade AB - 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. VL - 89 U4 - 052107 UR - http://journals.aps.org/pra/abstract/10.1103/PhysRevA.89.052107 CP - 5 U5 - http://dx.doi.org/10.1103/PhysRevA.89.052107 ER - TY - JOUR T1 - Robust Extraction of Tomographic Information via Randomized Benchmarking JF - Physical Review X Y1 - 2014 A1 - Shelby Kimmel A1 - Marcus P. da Silva A1 - Colm A. Ryan A1 - Blake R. Johnson A1 - Thomas Ohki AB - 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. VL - 4 UR - http://arxiv.org/abs/1306.2348v1 CP - 1 J1 - Phys. Rev. X U5 - 10.1103/PhysRevX.4.011050 ER - TY - JOUR T1 - Realizing Fractional Chern Insulators with Dipolar Spins JF - Physical Review Letters Y1 - 2013 A1 - Norman Y. Yao A1 - Alexey V. Gorshkov A1 - Chris R. Laumann A1 - Andreas M. Läuchli A1 - Jun Ye A1 - Mikhail D. Lukin AB - 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. VL - 110 UR - http://arxiv.org/abs/1212.4839v1 CP - 18 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.110.185302 ER - TY - JOUR T1 - The Resonant Exchange Qubit JF - Physical Review Letters Y1 - 2013 A1 - J. Medford A1 - J. Beil A1 - J. M. Taylor A1 - E. I. Rashba A1 - H. Lu A1 - A. C. Gossard A1 - C. M. Marcus AB - 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. VL - 111 UR - http://arxiv.org/abs/1304.3413v2 CP - 5 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.111.050501 ER - TY - JOUR T1 - Rank Reduction for the Local Consistency Problem JF - Journal of Mathematical Physics Y1 - 2012 A1 - Jianxin Chen A1 - Zhengfeng Ji A1 - Alexander Klyachko A1 - David W. Kribs A1 - Bei Zeng AB - We address the problem of how simple a solution can be for a given quantum local consistency instance. More specifically, we investigate how small the rank of the global density operator can be if the local constraints are known to be compatible. We prove that any compatible local density operators can be satisfied by a low rank global density operator. Then we study both fermionic and bosonic versions of the N-representability problem as applications. After applying the channel-state duality, we prove that any compatible local channels can be obtained through a global quantum channel with small Kraus rank. VL - 53 U4 - 022202 UR - http://arxiv.org/abs/1106.3235v2 CP - 2 J1 - J. Math. Phys. U5 - 10.1063/1.3685644 ER - TY - JOUR T1 - Reply to Comment on "Space-Time Crystals of Trapped Ions Y1 - 2012 A1 - Tongcang Li A1 - Zhe-Xuan Gong A1 - Zhang-qi Yin A1 - H. T. Quan A1 - Xiaobo Yin A1 - Peng Zhang A1 - L. -M. Duan A1 - Xiang Zhang AB - This is a reply to the comment from Patrick Bruno (arXiv:1211.4792) on our paper (Phys. Rev. Lett. 109, 163001 (2012)). UR - http://arxiv.org/abs/1212.6959v2 U5 - http://dx.doi.org/10.1103/PhysRevLett.109.163001 ER - TY - JOUR T1 - Resonant control of polar molecules in an optical lattice JF - Physical Review A Y1 - 2012 A1 - Thomas M. Hanna A1 - Eite Tiesinga A1 - William F. Mitchell A1 - Paul S. Julienne AB - We study the resonant control of two nonreactive polar molecules in an optical lattice site, focussing on the example of RbCs. Collisional control can be achieved by tuning bound states of the intermolecular dipolar potential, by varying the applied electric field or trap frequency. We consider a wide range of electric fields and trapping geometries, showing that a three-dimensional optical lattice allows for significantly wider avoided crossings than free space or quasi-two dimensional geometries. Furthermore, we find that dipolar confinement induced resonances can be created with reasonable trapping frequencies and electric fields, and have widths that will enable useful control in forthcoming experiments. VL - 85 UR - http://arxiv.org/abs/1111.0227v1 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.85.022703 ER - TY - JOUR T1 - Resolved atomic interaction sidebands in an optical clock transition JF - Physical Review Letters Y1 - 2011 A1 - Michael Bishof A1 - Yige Lin A1 - Matthew D. Swallows A1 - Alexey V. Gorshkov A1 - Jun Ye A1 - Ana Maria Rey AB - We report the observation of resolved atomic interaction sidebands (ISB) in the ${}^{87}$Sr optical clock transition when atoms at microkelvin temperatures are confined in a two-dimensional (2D) optical lattice. The ISB are a manifestation of the strong interactions that occur between atoms confined in a quasi-one-dimensional geometry and disappear when the confinement is relaxed along one dimension. The emergence of ISB is linked to the recently observed suppression of collisional frequency shifts in [1]. At the current temperatures, the ISB can be resolved but are broad. At lower temperatures, ISB are predicted to be substantially narrower and usable as powerful spectroscopic tools in strongly interacting alkaline-earth gases. VL - 106 UR - http://arxiv.org/abs/1102.1016v2 CP - 25 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.106.250801 ER - TY - JOUR T1 - Robust Quantum State Transfer in Random Unpolarized Spin Chains JF - Physical Review Letters Y1 - 2011 A1 - Norman Y. Yao A1 - Liang Jiang A1 - Alexey V. Gorshkov A1 - Zhe-Xuan Gong A1 - Alex Zhai A1 - L. -M. Duan A1 - Mikhail D. Lukin AB - We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between Nitrogen-Vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed. VL - 106 UR - http://arxiv.org/abs/1011.2762v2 CP - 4 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.106.040505 ER - TY - JOUR T1 - On the relationship between continuous- and discrete-time quantum walk JF - Communications in Mathematical Physics Y1 - 2010 A1 - Andrew M. Childs AB - 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. VL - 294 U4 - 581 - 603 UR - http://arxiv.org/abs/0810.0312v3 CP - 2 J1 - Commun. Math. Phys. U5 - 10.1007/s00220-009-0930-1 ER - TY - JOUR T1 - Realization of Coherent Optically Dense Media via Buffer-Gas Cooling JF - Physical Review A Y1 - 2009 A1 - Tao Hong A1 - Alexey V. Gorshkov A1 - David Patterson A1 - Alexander S. Zibrov A1 - John M. Doyle A1 - Mikhail D. Lukin A1 - Mara G. Prentiss AB - 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. VL - 79 UR - http://arxiv.org/abs/0805.1416v2 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.79.013806 ER - TY - JOUR T1 - Relaxation, dephasing, and quantum control of electron spins in double quantum dots JF - Physical Review B Y1 - 2007 A1 - J. M. Taylor A1 - J. R. Petta A1 - A. C. Johnson A1 - A. Yacoby A1 - C. M. Marcus A1 - M. D. Lukin AB - Recent experiments have demonstrated quantum manipulation of two-electron spin states in double quantum dots using electrically controlled exchange interactions. Here, we present a detailed theory for electron spin dynamics in two-electron double dot systems that was used to guide these experiments and analyze experimental results. The theory treats both charge and spin degrees of freedom on an equal basis. Specifically, we analyze the relaxation and dephasing mechanisms that are relevant to experiments and discuss practical approaches for quantum control of two-electron system. We show that both charge and spin dephasing play important roles in the dynamics of the two-spin system, but neither represents a fundamental limit for electrical control of spin degrees of freedom in semiconductor quantum bits. VL - 76 UR - http://arxiv.org/abs/cond-mat/0602470v2 CP - 3 J1 - Phys. Rev. B U5 - 10.1103/PhysRevB.76.035315 ER - TY - JOUR T1 - Relativistic many-body calculations of electric-dipole matrix elements, lifetimes and polarizabilities in rubidium JF - Physical Review A Y1 - 2004 A1 - M. S. Safronova A1 - Carl J. Williams A1 - Charles W. Clark AB - Electric-dipole matrix elements for ns-n'p, nd-n'p, and 6d-4f transitions in Rb are calculated using a relativistic all-order method. A third-order calculation is also carried out for these matrix elements to evaluate the importance of the high-order many-body perturbation theory contributions. The all-order matrix elements are used to evaluate lifetimes of ns and np levels with n=6, 7, 8 and nd levels with n=4, 5, 6 for comparison with experiment and to provide benchmark values for these lifetimes. The dynamic polarizabilities are calculated for ns states of rubidium. The resulting lifetime and polarizability values are compared with available theory and experiment. VL - 69 UR - http://arxiv.org/abs/physics/0307057v1 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.69.022509 ER - TY - JOUR T1 - Reversible simulation of bipartite product Hamiltonians JF - IEEE Transactions on Information Theory Y1 - 2004 A1 - Andrew M. Childs A1 - Debbie W. Leung A1 - Guifre Vidal AB - Consider two quantum systems A and B interacting according to a product Hamiltonian H = H_A x H_B. We show that any two such Hamiltonians can be used to simulate each other reversibly (i.e., without efficiency losses) with the help of local unitary operations and local ancillas. Accordingly, all non-local features of a product Hamiltonian -- including the rate at which it can be used to produce entanglement, transmit classical or quantum information, or simulate other Hamiltonians -- depend only upon a single parameter. We identify this parameter and use it to obtain an explicit expression for the entanglement capacity of all product Hamiltonians. Finally, we show how the notion of simulation leads to a natural formulation of measures of the strength of a nonlocal Hamiltonian. VL - 50 U4 - 1189 - 1197 UR - http://arxiv.org/abs/quant-ph/0303097v1 CP - 6 J1 - IEEE Trans. Inform. Theory U5 - 10.1109/TIT.2004.828069 ER - TY - JOUR T1 - Realization of quantum process tomography in NMR JF - Physical Review A Y1 - 2001 A1 - Andrew M. Childs A1 - Isaac L. Chuang A1 - Debbie W. Leung AB - Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-not logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying nearly all models of quantum error correction, the independence of errors on different qubits. VL - 64 UR - http://arxiv.org/abs/quant-ph/0012032v1 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.64.012314 ER - TY - JOUR T1 - Robustness of adiabatic quantum computation JF - Physical Review A Y1 - 2001 A1 - Andrew M. Childs A1 - Edward Farhi A1 - John Preskill AB - We study the fault tolerance of quantum computation by adiabatic evolution, a quantum algorithm for solving various combinatorial search problems. We describe an inherent robustness of adiabatic computation against two kinds of errors, unitary control errors and decoherence, and we study this robustness using numerical simulations of the algorithm. VL - 65 UR - http://arxiv.org/abs/quant-ph/0108048v1 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.65.012322 ER - TY - JOUR T1 - Randers surfaces whose Laplacians have completely positive symbol JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 1999 A1 - Bao, David A1 - Lackey, Brad VL - 38 U4 - 27–40 ER - TY - JOUR T1 - Revised Proof of the Uniqueness Theorem for 'No Collapse' Interpretations of Quantum Mechanics Y1 - 1999 A1 - Jeffrey Bub A1 - Rob Clifton A1 - Sheldon Goldstein AB - We show that the Bub-Clifton uniqueness theorem for 'no collapse' interpretations of quantum mechanics (Studies in the History and Philosophy of Modern Physics 27, 181-219 (1996)) can be proved without the 'weak separability' assumption. UR - http://arxiv.org/abs/quant-ph/9910097v1 J1 - Studies in History and Philosophy of Modern Physics 31 (2000) 95 ER -