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Uncertain fate of fair sampling in quantum annealing

Mario S. Könz, Guglielmo Mazzola, Andrew J. Ochoa, Helmut G. Katzgraber, and Matthias Troyer
Phys. Rev. A 100, 030303(R) – Published 20 September 2019

Abstract

Recently, it was demonstrated both theoretically and experimentally on the D-Wave quantum annealer that transverse-field quantum annealing does not find all ground states with equal probability. In particular, it was proposed that more complex driver Hamiltonians beyond transverse fields might mitigate this shortcoming. Here, we investigate the mechanisms of (un)fair sampling in quantum annealing. While higher-order terms can improve the sampling for selected small problems, we present multiple counterexamples where driver Hamiltonians that go beyond transverse fields do not remove the sampling bias. Using perturbation theory we explain why this is the case. In addition, we present large-scale quantum Monte Carlo simulations for spin glasses with known degeneracy in two space dimensions and demonstrate that the fair-sampling performance of quadratic driver terms is comparable to standard transverse-field drivers. Our results suggest that quantum annealing machines are not well suited for sampling applications, unless postprocessing techniques to improve the sampling are applied.

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  • Received 16 June 2018

DOI:https://doi.org/10.1103/PhysRevA.100.030303

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Mario S. Könz1,*, Guglielmo Mazzola1, Andrew J. Ochoa2, Helmut G. Katzgraber2,3,4, and Matthias Troyer1,5

  • 1Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
  • 2Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA
  • 31QB Information Technologies (1QBit), Vancouver, British Columbia, Canada V6B 4W4
  • 4Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
  • 5Microsoft Quantum, Microsoft, Redmond, Washington 98052, USA

  • *mkoenz@itp.phys.ethz.ch

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Issue

Vol. 100, Iss. 3 — September 2019

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