A quantum parallel Markov chain Monte Carlo

12/01/2021

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by   Andrew J. Holbrook, et al.

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We propose a novel quantum computing strategy for parallel MCMC algorithms that generate multiple proposals at each step. This strategy makes parallel MCMC amenable to quantum parallelization by using the Gumbel-max trick to turn the generalized accept-reject step into a discrete optimization problem. This 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^1/2). In the following, we review both the rudiments of quantum computing and the Gumbel-max trick in order to elucidate their combination for as wide a readership as possible.