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

TL;DR

This paper introduces a polynomial-time post-processing algorithm that enhances sampling fairness in optimization problems, improving the diversity of solutions obtained from quantum and classical methods, especially in biased sampling scenarios.

Contribution

The authors present a simple, rejection-free cluster update technique that improves sampling fairness for any optimization approach, including quantum annealers and classical algorithms.

Findings

Improves sampling fairness in quantum annealing data.

Enhances diversity of solutions in Ising spin glasses.

Effective even when including sub-optimal states.

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.