Feeding the multitude: A polynomial-time algorithm to improve sampling of degenerate optimization problems

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 employed algorithm. Here we present a simple post-processing technique that improves sampling for any optimization technique. Starting from a pool of known optima, 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 any new states can be found, the solution pool is typically increased. We illustrate our results on exponentially-biased data produced on the D-Wave 2X quantum annealer.