A Quantum Parallel Markov Chain Monte Carlo

Abstract

We propose a novel hybrid quantum computing strategy for parallel MCMC algorithms that generate multiple proposals at each step. This strategy makes the rate-limiting step within parallel MCMC amenable to quantum parallelization by using the Gumbel-max trick to turn the generalized accept-reject step into a discrete optimization problem. When combined with new insights from the parallel MCMC literature, such an approach allows us to embed target density evaluations within a well-known extension of Grover’s quantum search algorithm. Letting P denote the number of proposals in a single MCMC iteration, the combined strategy reduces the number of target evaluations required from O ( P ) to O ( P ) . In the following, we review the rudiments of quantum computing, quantum search and the Gumbel-max trick in order to elucidate their combination for as wide a readership as possible.