Quantum Annealing Enhanced Markov-Chain Monte Carlo

Abstract: In this study, we propose quantum annealing-enhanced Markov Chain Monte Carlo (QAEMCMC), where QA is integrated into the MCMC subroutine. QA efficiently explores low-energy configurations and overcomes local minima, enabling the generation of proposal states with a high acceptance probability. We benchmark QAEMCMC for the Sherrington-Kirkpatrick model and demonstrate its superior performance over the classical MCMC method. Our results reveal larger spectral gaps, faster convergence of energy observables, and reduced total variation distance between the empirical and target distributions. QAEMCMC accelerates MCMC and provides an efficient method for complex systems, paving the way for scalable quantum-assisted sampling strategies.