Feeding the multitude: A polynomial-time algorithm to improve sampling

Abstract

A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution space tends to be favored while, in the worst case, some solutions can never be accessed by the used algorithm. Here we present a simple post-processing technique that improves sampling for any optimization approach, either quantum or classical. More precisely, starting from a pool of a few optimal configurations, the algorithm generates potentially new solutions via rejection-free cluster updates at zero temperature. Although the method is not ergodic and there is no guarantee that all the solutions can be found, fair sampling is typically improved. We illustrate the effectiveness of our method by improving the exponentially biased data produced by the D-Wave 2X quantum annealer [Phys. Rev. Lett. 118, 07052 (2017)], as well as data from three-dimensional Ising spin glasses. As part of the study, we also show that sampling is improved when sub-optimal states are included and discuss sampling at a finite fixed temperature.

16 pages, 15 figures, 2 tables

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Cited by in corpus (7)

• Uncertain fate of fair sampling in quantum annealing
• From Ansätze to Z-gates: a NASA View of Quantum Computing
• Computational complexity of three-dimensional Ising spin glass: Lessons from D-Wave annealer
• Mapping State Transition Susceptibility in Quantum Annealing
• Biased Degenerate Ground-State Sampling of Small Ising Models with Converged QAOA
• Optimization and benchmarking of the thermal cycling algorithm
• Counting with the quantum alternating operator ansatz