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 ratelimiting step within parallel MCMC amenable to quantum parallelization by using the Gumbelmax trick to turn the generalized acceptreject 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 wellknown 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 $\mathcal{O}(P)$ to $\mathcal{O}(P^{1/2})$. In the following, we review the rudiments of quantum computing, quantum search and the Gumbelmax trick in order to elucidate their combination for as wide a readership as possible.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 DOI:
 10.48550/arXiv.2112.00212
 arXiv:
 arXiv:2112.00212
 Bibcode:
 2021arXiv211200212H
 Keywords:

 Quantum Physics;
 Statistics  Computation
 EPrint:
 To appear in JCGS