Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session B13: Adiabatic Quantum Computation and Quantum AnnealingInvited
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Sponsoring Units: GQI Chair: Tameem Albash, Univ of Southern California Room: 309 |
Monday, March 14, 2016 11:15AM - 11:51AM |
B13.00001: Simulated annealing versus quantum annealing Invited Speaker: Matthias Troyer Based on simulated classical annealing and simulated quantum annealing using quantum Monte Carlo (QMC) simulations I will explore the question where physical or simulated quantum annealers may outperform classical optimization algorithms. Although the stochastic dynamics of QMC simulations is not the same as the unitary dynamics of a quantum system, I will first show that for the problem of quantum tunneling between two local minima both QMC simulations and a physical system exhibit the same scaling of tunneling times with barrier height. The scaling in both cases is $O(\Delta^2)$, where $\Delta$ is the tunneling splitting. An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open instead of periodic boundary conditions in imaginary time, equivalent to a projector QMC algorithm, one obtains a quadratic speedup for QMC, and achieve linear scaling in $\Delta$ [1]. I will then address the apparent contradiction between experiments on a D-Wave 2 system that failed to see evidence of quantum speedup [2] and previous QMC results [3] that indicated an advantage of quantum annealing over classical annealing for spin glasses. We find that this contradiction is resolved by taking the continuous time limit in the QMC simulations which then agree with the experimentally observed behavior and show no speedup for 2D spin glasses. However, QMC simulations with large time steps gain further advantage: they ``cheat” by ignoring what happens during a (large) time step, and can thus outperform both simulated quantum annealers and classical annealers [4]. I will then address the question how to optimally run a simulated or physical quantum annealer. Investigating the behavior of the tails of the distribution of runtimes for very hard instances we find that adiabatically slow annealing is far from optimal. On the contrary, many repeated relatively fast annealing runs can be orders of magnitude faster for hard sin glass problems. The intuitive explanation is that hard instances, which are stuck in the “wrong” minimum can be solved faster by perturbing them [5]. I will finally discuss the consequences of these findings for designing better quantum annealers. [1] S.V. Isakov, G. Mazzola, V.N. Smelyanskiy, Z. Jiang, S. Boixo, H. Neven, and M. Troyer, arXiv:1510.08057. [2] T.F. R{\o}nnow, Z. Wang, J. Job, S. Boixo, S.V. Isakov, D. Wecker, J.M. Martinis, D.A. Lidar, M. Troyer, Science {\bf 345}, 420 (2014). [3] G.E. Santoro, R. Martonak, E. Tosatti, and R. Car, Science {\bf 295}, 2427 (2002). [4] B. Heim, T. F. R{\o}nnow, S. V. Isakov, and M. Troyer, Science {\bf 348}, 215 (2015) (2015). [5] D.S. Steiger, T.F. R{\o}nnow, M. Troyer, Phys. Rev. Lett. (in press); arXiv:1504.07991 [Preview Abstract] |
Monday, March 14, 2016 11:51AM - 12:27PM |
B13.00002: Mean-field analysis of quantum annealing with XX-type terms Invited Speaker: Hidetoshi Nishimori I analyze the role of XX-type terms in quantum annealing for a few mean-field systems including the Ising ferromagnet and the Hopfield model, both with many-body interactions. The XX-type terms are shown to be effective to remove first-order quantum phase transitions, which exist in the conventional implementation of quantum annealing using only transverse fields. This means an exponential increase in efficiency, and is suggestive for the design of quantum annealers. I will discuss how and why this phenomenon emerges and what may happen on realistic finite-dimensional lattices. \newline [1] Y. Seki and H. Nishimori, J. Phys. A 48, 335301 (2015). \newline [2] B. Seoane and H. Nishimori, J. Phys. A 45, 435301 (2012). \newline [3] Y. Seki and H. Nishimori, Phys. Rev. E 85, 051112 (2012). \newline [4] S. Suzuki, H. Nishimori and M. Suzuki, Phys. Rev. E 75, 051112 (2007). [Preview Abstract] |
Monday, March 14, 2016 12:27PM - 1:03PM |
B13.00003: Error suppression and correction for quantum annealing Invited Speaker: Daniel Lidar \noindent While adiabatic quantum computing and quantum annealing enjoy a certain degree of inherent robustness against excitations and control errors, there is no escaping the need for error correction or suppression. In this talk I will give an overview of our work on the development of such error correction and suppression methods. We have experimentally tested one such method combining encoding, energy penalties and decoding, on a D-Wave Two processor, with encouraging results. Mean field theory shows that this can be explained in terms of a softening of the closing of the gap due to the energy penalty, resulting in protection against excitations that occur near the quantum critical point. Decoding recovers population from excited states and enhances the success probability of quantum annealing. Moreover, we have demonstrated that using repetition codes with increasing code distance can lower the effective temperature of the annealer. \\\\ \noindent References:\\ \noindent - K.L. Pudenz, T. Albash, D.A. Lidar, “Error corrected quantum annealing with hundreds of qubits”, Nature Commun. 5, 3243 (2014).\\ \noindent - K.L. Pudenz, T. Albash, D.A. Lidar, “Quantum annealing correction for random Ising problems”, Phys. Rev. A. 91, 042302 (2015).\\ \noindent - S. Matsuura, H. Nishimori, T. Albash, D.A. Lidar, “Mean Field Analysis of Quantum Annealing Correction”. arXiv:1510.07709.\\ \noindent - W. Vinci et al., in preparation. [Preview Abstract] |
Monday, March 14, 2016 1:03PM - 1:39PM |
B13.00004: Precision and the approach to optimality in quantum annealing processors Invited Speaker: Mark W Johnson The last few years have seen both a significant technological advance towards the practical application of, and a growing scientific interest in the underlying behaviour of quantum annealing (QA) algorithms [1]. A series of commercially available QA processors, most recently the D-Wave 2X$^\mathrm{TM}$ 1000 qubit processor, have provided a valuable platform for empirical study of QA at a non-trivial scale. From this it has become clear that misspecification of Hamiltonian parameters is an important performance consideration, both for the goal of studying the underlying physics of QA, as well as that of building a practical and useful QA processor. The empirical study of the physics of QA requires a way to look beyond Hamiltonian misspecification.\par Recently, a solver metric called 'time-to-target' was proposed [2] as a way to compare quantum annealing processors to classical heuristic algorithms. This approach puts emphasis on analyzing a solver's short time approach to the ground state. In this presentation I will review the processor technology, based on superconducting flux qubits, and some of the known sources of error in Hamiltonian specification. I will then discuss recent advances in reducing Hamiltonian specification error, as well as review the time-to-target metric and empirical results analyzed in this way.\par [1] E.g. "Discussion and Debate: Quantum Annealing: The Fastest Route to Quantum Computation?", S Suzuki and A Das eds., Eur. Phys. J. Special Topics, 224 (1), Feb 2015.\par [2] J. King, et al.; "Benchmarking a [QA] processor with the time-to-target metric", arXiv:1508.05087 [quant-ph] [Preview Abstract] |
Monday, March 14, 2016 1:39PM - 2:15PM |
B13.00005: Universal fault-tolerant adiabatic quantum computing with quantum dots or donors Invited Speaker: Andrew Landahl I will present a conceptual design for an adiabatic quantum computer that can achieve arbitrarily accurate universal fault-tolerant quantum computations with a constant energy gap and nearest-neighbor interactions. This machine can run any quantum algorithm known today or discovered in the future, in principle. The key theoretical idea is adiabatic deformation of degenerate ground spaces formed by topological quantum error-correcting codes. An open problem with the design is making the four-body interactions and measurements it uses more technologically accessible. I will present some partial solutions, including one in which interactions between quantum dots or donors in a two-dimensional array can emulate the desired interactions in second-order perturbation theory. I will conclude with some open problems, including the challenge of reformulating Kitaev's gadget perturbation theory technique so that it preserves fault tolerance. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
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