Boltzmann sampling with quantum annealers via fast Stein correction

TL;DR

This paper introduces a fast Stein correction method using random features and gradient updates to improve Boltzmann sampling accuracy with quantum annealers, potentially rivaling MCMC methods.

Contribution

It develops an efficient approximation technique for Stein correction tailored to quantum annealers, enabling more accurate thermal average calculations.

Findings

Significant reduction in residual error of thermal averages.

Method enables quantum annealers to serve as a practical alternative to MCMC.

Benchmarking shows improved sampling accuracy.

Abstract

Despite the attempts to apply a quantum annealer to Boltzmann sampling, it is still impossible to perform accurate sampling at arbitrary temperatures. Conventional distribution correction methods such as importance sampling and resampling cannot be applied, because the analytical expression of sampling distribution is unknown for a quantum annealer. Stein correction (Liu and Lee, 2017) can correct the samples by weighting without the knowledge of the sampling distribution, but the naive implementation requires the solution of a large-scale quadratic program, hampering usage in practical problems. In this letter, a fast and approximate method based on random feature map and exponentiated gradient updates is developed to compute the sample weights, and used to correct the samples generated by D-Wave quantum annealers. In benchmarking problems, it is observed that the residual error of thermal average calculations is reduced significantly. If combined with our method, quantum annealers may emerge as a viable alternative to long-established Markov chain Monte Carlo methods.