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 PdenotethenumberofproposalsinasingleMCMCiteration,thecombinedstrategyreducesthenumberoftargetevaluationsrequiredfrom𝒪(P)to𝒪P1/2. 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.