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 quantum annealer chimera topology. In addition, a simple heuristic to approximate the number of solutions of a degenerate problem is introduced.
- Received 18 March 2019
DOI:https://doi.org/10.1103/PhysRevE.99.063314
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