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Finite temperature quantum annealing solving exponentially small gap problem with non-monotonic success probability

Author

Listed:
  • Anurag Mishra

    (University of Southern California
    University of Southern California)

  • Tameem Albash

    (University of Southern California
    University of Southern California
    University of Southern California)

  • Daniel A. Lidar

    (University of Southern California
    University of Southern California
    University of Southern California
    University of Southern California)

Abstract

Closed-system quantum annealing is expected to sometimes fail spectacularly in solving simple problems for which the gap becomes exponentially small in the problem size. Much less is known about whether this gap scaling also impedes open-system quantum annealing. Here, we study the performance of a quantum annealing processor in solving such a problem: a ferromagnetic chain with sectors of alternating coupling strength that is classically trivial but exhibits an exponentially decreasing gap in the sector size. The gap is several orders of magnitude smaller than the device temperature. Contrary to the closed-system expectation, the success probability rises for sufficiently large sector sizes. The success probability is strongly correlated with the number of thermally accessible excited states at the critical point. We demonstrate that this behavior is consistent with a quantum open-system description that is unrelated to thermal relaxation, and is instead dominated by the system’s properties at the critical point.

Suggested Citation

  • Anurag Mishra & Tameem Albash & Daniel A. Lidar, 2018. "Finite temperature quantum annealing solving exponentially small gap problem with non-monotonic success probability," Nature Communications, Nature, vol. 9(1), pages 1-8, December.
    • Handle: RePEc:nat:natcom:v:9:y:2018:i:1:d:10.1038_s41467-018-05239-9
    DOI: 10.1038/s41467-018-05239-9
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    Cited by:

    1. X. Dai & R. Trappen & H. Chen & D. Melanson & M. A. Yurtalan & D. M. Tennant & A. J. Martinez & Y. Tang & E. Mozgunov & J. Gibson & J. A. Grover & S. M. Disseler & J. I. Basham & S. Novikov & R. Das &, 2025. "Dissipative Landau-Zener tunneling in the crossover regime from weak to strong environment coupling," Nature Communications, Nature, vol. 16(1), pages 1-10, December.

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