Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone. This motivates us to introduce \emph{measurement-only models}, in which the "scrambling" and "un-scrambling" effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes. This represents a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits. We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models. We find that the principle driving the EPTs in these models is \emph{frustration}, or mutual incompatibility, of the measurements. Suprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local (≳3-body) operators. We identify a class of exceptions to this behavior ("bipartite ensembles") which cannot sustain an entangling phase, but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points. Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light-cone, despite the non-locality inherent to quantum measurements.

VL - 11 UR - https://arxiv.org/abs/2004.09560 CP - 1 J1 - Phys. Rev. X U5 - 10.1103/PhysRevX.11.011030 ER - TY - JOUR T1 - Learnability of the output distributions of local quantum circuits Y1 - 2021 A1 - Marcel Hinsche A1 - Marios Ioannou A1 - Alexander Nietner A1 - Jonas Haferkamp A1 - Yihui Quek A1 - Dominik Hangleiter A1 - Jean-Pierre Seifert A1 - Jens Eisert A1 - Ryan Sweke AB -There is currently a large interest in understanding the potential advantages quantum devices can offer for probabilistic modelling. In this work we investigate, within two different oracle models, the probably approximately correct (PAC) learnability of quantum circuit Born machines, i.e., the output distributions of local quantum circuits. We first show a negative result, namely, that the output distributions of super-logarithmic depth Clifford circuits are not sample-efficiently learnable in the statistical query model, i.e., when given query access to empirical expectation values of bounded functions over the sample space. This immediately implies the hardness, for both quantum and classical algorithms, of learning from statistical queries the output distributions of local quantum circuits using any gate set which includes the Clifford group. As many practical generative modelling algorithms use statistical queries -- including those for training quantum circuit Born machines -- our result is broadly applicable and strongly limits the possibility of a meaningful quantum advantage for learning the output distributions of local quantum circuits. As a positive result, we show that in a more powerful oracle model, namely when directly given access to samples, the output distributions of local Clifford circuits are computationally efficiently PAC learnable by a classical learner. Our results are equally applicable to the problems of learning an algorithm for generating samples from the target distribution (generative modelling) and learning an algorithm for evaluating its probabilities (density modelling). They provide the first rigorous insights into the learnability of output distributions of local quantum circuits from the probabilistic modelling perspective.

UR - https://arxiv.org/abs/2110.05517 ER - TY - JOUR T1 - Quantum Computational Supremacy via High-Dimensional Gaussian Boson Sampling Y1 - 2021 A1 - Abhinav Deshpande A1 - Arthur Mehta A1 - Trevor Vincent A1 - Nicolas Quesada A1 - Marcel Hinsche A1 - Marios Ioannou A1 - Lars Madsen A1 - Jonathan Lavoie A1 - Haoyu Qi A1 - Jens Eisert A1 - Dominik Hangleiter A1 - Bill Fefferman A1 - Ish Dhand AB -Photonics is a promising platform for demonstrating quantum computational supremacy (QCS) by convincingly outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing photonics proposals and demonstrations face significant hurdles. Experimentally, current implementations of Gaussian boson sampling lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make significant progress in improving both the theoretical evidence and experimental prospects. On the theory side, we provide strong evidence for the hardness of Gaussian boson sampling, placing it on par with the strongest theoretical proposals for QCS. On the experimental side, we propose a new QCS architecture, high-dimensional Gaussian boson sampling, which is programmable and can be implemented with low loss rates using few optical components. We show that particular classical algorithms for simulating GBS are vastly outperformed by high-dimensional Gaussian boson sampling experiments at modest system sizes. This work thus opens the path to demonstrating QCS with programmable photonic processors.

UR - https://arxiv.org/abs/2102.12474 ER - TY - JOUR T1 - Quench Dynamics of a Fermi Gas with Strong Long-Range Interactions JF - Phys. Rev. X Y1 - 2021 A1 - Elmer Guardado-Sanchez A1 - Benjamin M. Spar A1 - Peter Schauss A1 - Ron Belyansky A1 - Jeremy T. Young A1 - Przemyslaw Bienias A1 - Alexey V. Gorshkov A1 - Thomas Iadecola A1 - Waseem S. Bakr AB -We induce strong non-local interactions in a 2D Fermi gas in an optical lattice using Rydberg dressing. The system is approximately described by a t−V model on a square lattice where the fermions experience isotropic nearest-neighbor interactions and are free to hop only along one direction. We measure the interactions using many-body Ramsey interferometry and study the lifetime of the gas in the presence of tunneling, finding that tunneling does not reduce the lifetime. To probe the interplay of non-local interactions with tunneling, we investigate the short-time relaxation dynamics of charge density waves in the gas. We find that strong nearest-neighbor interactions slow down the relaxation. Our work opens the door for quantum simulations of systems with strong non-local interactions such as extended Fermi-Hubbard models.

VL - 11 UR - https://arxiv.org/abs/2010.05871 U5 - https://doi.org/10.1103/PhysRevX.11.021036 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 - Hilbert-Space Fragmentation from Strict Confinement JF - Phys. Rev. Lett. Y1 - 2020 A1 - Zhi-Cheng Yang A1 - Fangli Liu A1 - Alexey V. Gorshkov A1 - Thomas Iadecola AB -We study one-dimensional spin-1/2 models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most of the previous works emphasize dipole moment conservation as an essential ingredient for such fragmentation, we instead require two commuting U(1) conserved quantities associated with the total domain-wall number and the total magnetization. The latter arises naturally from the confinement of domain walls. Remarkably, while some connected components of the Hilbert space thermalize, others are integrable by Bethe ansatz. We further demonstrate how this Hilbert-space fragmentation pattern arises perturbatively in the confining limit of Z2 gauge theory coupled to fermionic matter, leading to a hierarchy of time scales for motion of the fermions. This model can be realized experimentally in two complementary settings.

VL - 124 UR - https://arxiv.org/abs/1912.04300 CP - 207602 U5 - https://doi.org/10.1103/PhysRevLett.124.207602 ER - TY - JOUR T1 - Localization and criticality in antiblockaded 2D Rydberg atom arrays Y1 - 2020 A1 - Fangli Liu A1 - Zhi-Cheng Yang A1 - Przemyslaw Bienias A1 - Thomas Iadecola A1 - Alexey V. Gorshkov AB -Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under anti-blockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime's existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.

UR - https://arxiv.org/abs/2012.03946 ER - TY - JOUR T1 - Probing XY phase transitions in a Josephson junction array with tunable frustration Y1 - 2020 A1 - R. Cosmic A1 - K. Kawabata A1 - Y. Ashida A1 - H. Ikegami A1 - S. Furukawa A1 - P. Patil A1 - J. M. Taylor A1 - Y. Nakamura AB -The seminal theoretical works of Berezinskii, Kosterlitz, and Thouless presented a new paradigm for phase transitions in condensed matter that are driven by topological excitations. These transitions have been extensively studied in the context of two-dimensional XY models -- coupled compasses -- and have generated interest in the context of quantum simulation. Here, we use a circuit quantum-electrodynamics architecture to study the critical behavior of engineered XY models through their dynamical response. In particular, we examine not only the unfrustrated case but also the fully-frustrated case which leads to enhanced degeneracy associated with the spin rotational [U(1)] and discrete chiral (Z2) symmetries. The nature of the transition in the frustrated case has posed a challenge for theoretical studies while direct experimental probes remain elusive. Here we identify the transition temperatures for both the unfrustrated and fully-frustrated XY models by probing a Josephson junction array close to equilibrium using weak microwave excitations and measuring the temperature dependence of the effective damping obtained from the complex reflection coefficient. We argue that our probing technique is primarily sensitive to the dynamics of the U(1) part.

UR - https://arxiv.org/abs/2001.07877 ER - TY - JOUR T1 - Probing ground-state phase transitions through quench dynamics JF - Phys. Rev. Lett. Y1 - 2019 A1 - Paraj Titum A1 - Joseph T. Iosue A1 - James R. Garrison A1 - Alexey V. Gorshkov A1 - Zhe-Xuan Gong AB -The 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.

VL - 123 UR - https://arxiv.org/abs/1809.06377 CP - 115701 U5 - https://doi.org/10.1103/PhysRevLett.123.115701 ER - TY - JOUR T1 - Programmable Quantum Simulations of Spin Systems with Trapped Ions Y1 - 2019 A1 - C. Monroe A1 - W. C. Campbell A1 - L. -M. Duan A1 - Z. -X. Gong A1 - Alexey V. Gorshkov A1 - P. Hess A1 - R. Islam A1 - K. Kim A1 - G. Pagano A1 - P. Richerme A1 - C. Senko A1 - N. Y. Yao AB -Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By applying optical fields that exert optical dipole forces on the ions, their Coulomb interaction can be modulated in ways that give rise to long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields. Here we review the theoretical mapping of atomic ions to interacting spin systems, the experimental preparation of complex equilibrium states, and the study of dynamical processes of this many-body interacting quantum system. The use of such quantum simulators for studying spin models may inform our understanding of exotic quantum materials and shed light on interacting quantum systems that cannot be modeled with conventional computers.

UR - https://arxiv.org/abs/1912.07845 ER - TY - JOUR T1 - Circuit QED-based measurement of vortex lattice order in a Josephson junction array JF - Phys. Rev. B 98, 060501 Y1 - 2018 A1 - R. Cosmic A1 - Hiroki Ikegami A1 - Zhirong Lin A1 - Kunihiro Inomata A1 - J. M. Taylor A1 - Yasunobu Nakamura AB -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.

UR - https://arxiv.org/abs/1803.04113 U5 - https://doi.org/10.1103/PhysRevB.98.060501 ER - TY - JOUR T1 - Electro-mechano-optical NMR detection JF - Optica Y1 - 2018 A1 - Kazuyuki Takeda A1 - Kentaro Nagasaka A1 - Atsushi Noguchi A1 - Rekishu Yamazaki A1 - Yasunobu Nakamura A1 - Eiji Iwase A1 - J. M. Taylor A1 - Koji Usami AB -Signal 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.

VL - 5 U4 - 152-158 UR - https://www.osapublishing.org/optica/abstract.cfm?uri=optica-5-2-152 CP - 2 U5 - 10.1364/OPTICA.5.000152 ER - TY - JOUR T1 - High-Order Multipole Radiation from Quantum Hall States in Dirac Materials JF - Physical Review B Y1 - 2017 A1 - Michael Gullans A1 - J. M. Taylor A1 - Atac Imamoglu A1 - Pouyan Ghaemi A1 - Mohammad Hafezi AB -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.

VL - 95 U4 - 235439 UR - https://arxiv.org/abs/1701.03464 CP - 23 U5 - 10.1103/PhysRevB.95.235439 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 - Mapping constrained optimization problems to quantum annealing with application to fault diagnosis Y1 - 2016 A1 - Bian, Zhengbing A1 - Chudak, Fabian A1 - Israel, Robert A1 - Lackey, Brad A1 - Macready, William G A1 - Roy, Aidan AB - 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. UR - http://arxiv.org/abs/1603.03111 ER - TY - JOUR T1 - Mapping contrained optimization problems to quantum annealing with application to fault diagnosis JF - Frontiers in ICT Y1 - 2016 A1 - Bian, Zhengbing A1 - Chudak, Fabian A1 - Robert Brian Israel A1 - Brad Lackey A1 - Macready, William G A1 - Aiden Roy AB -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. 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.

VL - 3 U4 - 14 UR - http://journal.frontiersin.org/article/10.3389/fict.2016.00014/full ER - TY - JOUR T1 - Discrete optimization using quantum annealing on sparse Ising models JF - Frontiers in Physics Y1 - 2014 A1 - Bian, Zhengbing A1 - Chudak, Fabian A1 - Israel, Robert A1 - Brad Lackey A1 - Macready, William G A1 - Roy, Aidan AB - This paper discusses techniques for solving discrete optimization problems using quantum annealing. Practical issues likely to affect the computation include precision limitations, finite temperature, bounded energy range, sparse connectivity, and small numbers of qubits. To address these concerns we propose a way of finding energy representations with large classical gaps between ground and first excited states, efficient algorithms for mapping non-compatible Ising models into the hardware, and the use of decomposition methods for problems that are too large to fit in hardware. We validate the approach by describing experiments with D-Wave quantum hardware for low density parity check decoding with up to 1000 variables. PB - Frontiers VL - 2 U4 - 56 ER - TY - JOUR T1 - Quantum computation of discrete logarithms in semigroups JF - Journal of Mathematical Cryptology Y1 - 2014 A1 - Andrew M. Childs A1 - Gábor Ivanyos AB - 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. VL - 8 UR - http://arxiv.org/abs/1310.6238v2 CP - 4 J1 - Journal of Mathematical Cryptology 8 U5 - 10.1515/jmc-2013-0038 ER - TY - JOUR T1 - Quantum Catalysis of Magnetic Phase Transitions in a Quantum Simulator JF - Physical Review Letters Y1 - 2013 A1 - Philip Richerme A1 - Crystal Senko A1 - Simcha Korenblit A1 - Jacob Smith A1 - Aaron Lee A1 - Rajibul Islam A1 - Wesley C. Campbell A1 - Christopher Monroe AB - 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. VL - 111 UR - http://arxiv.org/abs/1303.6983v2 CP - 10 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.111.100506 ER - TY - JOUR T1 - Quantum Simulation of Spin Models on an Arbitrary Lattice with Trapped Ions JF - New Journal of Physics Y1 - 2012 A1 - Simcha Korenblit A1 - Dvir Kafri A1 - Wess C. Campbell A1 - Rajibul Islam A1 - Emily E. Edwards A1 - Zhe-Xuan Gong A1 - Guin-Dar Lin A1 - Luming Duan A1 - Jungsang Kim A1 - Kihwan Kim A1 - Christopher Monroe AB - A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range effective spin-spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. Here we show how appropriate design of laser fields can provide for arbitrary multidimensional spin-spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently existing trap technology and is scalable to levels where classical methods of simulation are intractable. VL - 14 U4 - 095024 UR - http://arxiv.org/abs/1201.0776v1 CP - 9 J1 - New J. Phys. U5 - 10.1088/1367-2630/14/9/095024 ER - TY - JOUR T1 - Quantum information processing using localized ensembles of nuclear spins Y1 - 2004 A1 - J. M. Taylor A1 - G. Giedke A1 - H. Christ A1 - B. Paredes A1 - J. I. Cirac A1 - P. Zoller A1 - M. D. Lukin A1 - A. Imamoglu AB - We describe a technique for quantum information processing based on localized en sembles of nuclear spins. A qubit is identified as the presence or absence of a collective excitation of a mesoscopic ensemble of nuclear spins surrounding a single quantum dot. All single and two-qubit operations can be effected using hyperfine interactions and single-electron spin rotations, hence the proposed scheme avoids gate errors arising from entanglement between spin and orbital degrees of freedom. Ultra-long coherence times of nuclear spins suggest that this scheme could be particularly well suited for applications where long lived memory is essential. UR - http://arxiv.org/abs/cond-mat/0407640v2 ER - TY - JOUR T1 - Controlling a mesoscopic spin environment by quantum bit manipulation JF - Physical Review Letters Y1 - 2003 A1 - J. M. Taylor A1 - A. Imamoglu A1 - M. D. Lukin AB - We present a unified description of cooling and manipulation of a mesoscopic bath of nuclear spins via coupling to a single quantum system of electronic spin (quantum bit). We show that a bath cooled by the quantum bit rapidly saturates. Although the resulting saturated states of the spin bath (``dark states'') generally have low degrees of polarization and purity, their symmetry properties make them a valuable resource for the coherent manipulation of quantum bits. Specifically, we demonstrate that the dark states of nuclear ensembles can be used to coherently control the system-bath interaction and to provide a robust, long-lived quantum memory for qubit states. VL - 91 UR - http://arxiv.org/abs/cond-mat/0308459v1 CP - 24 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.91.246802 ER -