Fair sampling of ground-state configurations of binary optimization problems

Zheng Zhu; Andrew J. Ochoa; Helmut G. Katzgraber

doi:10.1103/physreve.99.063314

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arXiv · 1903.07600

Fair sampling of ground-state configurations of binary optimization problems

Zheng Zhu·Andrew J. Ochoa·Helmut G. Katzgraber

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Abstract

Although many efficient heuristics have been developed to solve binary optimization problems, these typically produce correlated solutions for degenerate problems. Most notably, transverse-field quantum annealing - the heuristic employed in current commercially-available quantum annealing machines - has been shown to often be exponentially biased when sampling the solution space. Here we present an approach to sample ground-state (or low-energy) configurations for binary optimization problems. The method samples degenerate states with almost equal probability and is based on a combination of parallel tempering Monte Carlo with isoenergetic cluster moves. We illustrate the approach using two-dimensional Ising spin glasses, as well as spin glasses on the D-Wave Systems Inc. quantum annealer chimera topology. In addition, a simple heuristic to approximate the number of solutions of a degenerate problem is introduced.

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Zheng Zhu, Andrew J. Ochoa, Helmut G. Katzgraber. 2019-06-26. Fair sampling of ground-state configurations of binary optimization problems. https://doi.org/10.1103/physreve.99.063314

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