Superconductivity provides a canonical example of a quantum phase of matter. When superconducting islands are connected by Josephson junctions in a lattice, the low temperature state of the system can map to the celebrated XY model and its associated universality classes. This has been used to experimentally implement realizations of Mott insulator and Berezinskii--Kosterlitz--Thouless (BKT) transitions to vortex dynamics analogous to those in type-II superconductors. When an external magnetic field is added, the effective spins of the XY model become frustrated, leading to the formation of topological defects (vortices). Here we observe the many-body dynamics of such an array, including frustration, via its coupling to a superconducting microwave cavity. We take the design of the transmon qubit, but replace the single junction between two antenna pads with the complete array. This allows us to probe the system at 10 mK with minimal self-heating by using weak coherent states at the single (microwave) photon level to probe the resonance frequency of the cavity. We observe signatures of ordered vortex lattice at rational flux fillings of the array.

%B Phys. Rev. B 98, 060501 %8 2018/03/12 %G eng %U https://arxiv.org/abs/1803.04113 %R https://doi.org/10.1103/PhysRevB.98.060501 %0 Journal Article %J Optica %D 2018 %T Electro-mechano-optical NMR detection %A Kazuyuki Takeda %A Kentaro Nagasaka %A Atsushi Noguchi %A Rekishu Yamazaki %A Yasunobu Nakamura %A Eiji Iwase %A Jacob M. Taylor %A Koji Usami %XSignal reception of nuclear magnetic resonance (NMR) usually relies on electrical amplification of the electromotive force caused by nuclear induction. Here, we report up-conversion of a radio-frequency NMR signal to an optical regime using a high-stress silicon nitride membrane that interfaces the electrical detection circuit and an optical cavity through the electro-mechanical and the opto-mechanical couplings. This enables optical NMR detection without sacrificing the versatility of the traditional nuclear induction approach. While the signal-to-noise ratio is currently limited by the Brownian motion of the membrane as well as additional technical noise, we find it can exceed that of the conventional electrical schemes by increasing the electro-mechanical coupling strength. The electro-mechano-optical NMR detection presented here can even be combined with the laser cooling technique applied to nuclear spins.

%B Optica %V 5 %P 152-158 %8 2018/02/01 %G eng %U https://www.osapublishing.org/optica/abstract.cfm?uri=optica-5-2-152 %N 2 %R 10.1364/OPTICA.5.000152 %0 Journal Article %D 2018 %T Probing ground-state phase transitions through quench dynamics %A Paraj Titum %A Joseph T. Iosue %A James R. Garrison %A Alexey V. Gorshkov %A Zhe-Xuan Gong %XThe study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a non-analytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal time scales. Therefore, our method can be used to approximately locate the quantum critical point. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.

%G eng %U https://arxiv.org/abs/1809.06377 %0 Journal Article %J Physical Review B %D 2017 %T High-Order Multipole Radiation from Quantum Hall States in Dirac Materials %A Michael Gullans %A Jacob M. Taylor %A Atac Imamoglu %A Pouyan Ghaemi %A Mohammad Hafezi %XTopological states can exhibit electronic coherence on macroscopic length scales. When the coherence length exceeds the wavelength of light, one can expect new phenomena to occur in the optical response of these states. We theoretically characterize this limit for integer quantum Hall states in two-dimensional Dirac materials. We find that the radiation from the bulk is dominated by dipole emission, whose spectral properties vary with the local disorder potential. On the other hand, the radiation from the edge is characterized by large multipole moments in the far-field associated with the efficient transfer of angular momentum from the electrons into the scattered light. These results demonstrate that high-order multipole transitions are a necessary component for the optical spectroscopy and control of quantum Hall and related topological states in electronic systems.

%B Physical Review B %V 95 %P 235439 %8 2017/06/30 %G eng %U https://arxiv.org/abs/1701.03464 %N 23 %R 10.1103/PhysRevB.95.235439 %0 Journal Article %D 2017 %T On the readiness of quantum optimization machines for industrial applications %A Alejandro Perdomo-Ortiz %A Alexander Feldman %A Asier Ozaeta %A Sergei V. Isakov %A Zheng Zhu %A Bryan O'Gorman %A Helmut G. Katzgraber %A Alexander Diedrich %A Hartmut Neven %A Johan de Kleer %A Brad Lackey %A Rupak Biswas %XThere have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for near-term quantum annealers.

%8 2017/08/31 %G eng %U https://arxiv.org/abs/1708.09780 %0 Journal Article %D 2016 %T Mapping constrained optimization problems to quantum annealing with application to fault diagnosis %A Bian, Zhengbing %A Chudak, Fabian %A Israel, Robert %A Lackey, Brad %A Macready, William G %A Roy, Aidan %X Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally-structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. In contrast, global embedding techniques generate a hardware independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of D-Wave's QA hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D-Wave's hardware to circuit-based fault-diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Further, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware. %G eng %U http://arxiv.org/abs/1603.03111 %0 Journal Article %J Frontiers in ICT %D 2016 %T Mapping contrained optimization problems to quantum annealing with application to fault diagnosis %A Bian, Zhengbing %A Chudak, Fabian %A Robert Brian Israel %A Brad Lackey %A Macready, William G %A Aiden Roy %XCurrent quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping Boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular, we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. By contrast, global embedding techniques generate a hardware-independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of the D-Wave hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D- Wave’s QA hardware to circuit-based fault diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000 N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Furthermore, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware.

%B Frontiers in ICT %V 3 %P 14 %8 2016/07/28 %G eng %U http://journal.frontiersin.org/article/10.3389/fict.2016.00014/full %0 Journal Article %J Frontiers in Physics %D 2014 %T Discrete optimization using quantum annealing on sparse Ising models %A Bian, Zhengbing %A Chudak, Fabian %A Israel, Robert %A Brad Lackey %A Macready, William G %A Roy, Aidan %X 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. %B Frontiers in Physics %I Frontiers %V 2 %P 56 %8 2014/09/01 %G eng %0 Journal Article %J Journal of Mathematical Cryptology %D 2014 %T Quantum computation of discrete logarithms in semigroups %A Andrew M. Childs %A GĂˇbor Ivanyos %X We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete logarithms in semigroups are insecure against quantum attacks. In contrast, we show that some generalizations of the discrete log problem are hard in semigroups despite being easy in groups. We relate a shifted version of the discrete log problem in semigroups to the dihedral hidden subgroup problem, and we show that the constructive membership problem with respect to $k \ge 2$ generators in a black-box abelian semigroup of order $N$ requires $\tilde \Theta(N^{\frac{1}{2}-\frac{1}{2k}})$ quantum queries. %B Journal of Mathematical Cryptology %V 8 %8 2014/01/1 %G eng %U http://arxiv.org/abs/1310.6238v2 %N 4 %! Journal of Mathematical Cryptology 8 %R 10.1515/jmc-2013-0038 %0 Journal Article %J Physical Review Letters %D 2013 %T Quantum Catalysis of Magnetic Phase Transitions in a Quantum Simulator %A Philip Richerme %A Crystal Senko %A Simcha Korenblit %A Jacob Smith %A Aaron Lee %A Rajibul Islam %A Wesley C. Campbell %A Christopher Monroe %X We control quantum fluctuations to create the ground state magnetic phases of a classical Ising model with a tunable longitudinal magnetic field using a system of 6 to 10 atomic ion spins. Due to the long-range Ising interactions, the various ground state spin configurations are separated by multiple first-order phase transitions, which in our zero temperature system cannot be driven by thermal fluctuations. We instead use a transverse magnetic field as a quantum catalyst to observe the first steps of the complete fractal devil's staircase, which emerges in the thermodynamic limit and can be mapped to a large number of many-body and energy-optimization problems. %B Physical Review Letters %V 111 %8 2013/9/5 %G eng %U http://arxiv.org/abs/1303.6983v2 %N 10 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.111.100506 %0 Journal Article %J New Journal of Physics %D 2012 %T Quantum Simulation of Spin Models on an Arbitrary Lattice with Trapped Ions %A Simcha Korenblit %A Dvir Kafri %A Wess C. Campbell %A Rajibul Islam %A Emily E. Edwards %A Zhe-Xuan Gong %A Guin-Dar Lin %A Luming Duan %A Jungsang Kim %A Kihwan Kim %A Christopher Monroe %X 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. %B New Journal of Physics %V 14 %P 095024 %8 2012/09/27 %G eng %U http://arxiv.org/abs/1201.0776v1 %N 9 %! New J. Phys. %R 10.1088/1367-2630/14/9/095024 %0 Journal Article %D 2004 %T Quantum information processing using localized ensembles of nuclear spins %A J. M. Taylor %A G. Giedke %A H. Christ %A B. Paredes %A J. I. Cirac %A P. Zoller %A M. D. Lukin %A A. Imamoglu %X 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. %8 2004/07/23 %G eng %U http://arxiv.org/abs/cond-mat/0407640v2 %0 Journal Article %J Physical Review Letters %D 2003 %T Controlling a mesoscopic spin environment by quantum bit manipulation %A J. M. Taylor %A A. Imamoglu %A M. D. Lukin %X 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. %B Physical Review Letters %V 91 %8 2003/12/10 %G eng %U http://arxiv.org/abs/cond-mat/0308459v1 %N 24 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.91.246802