Quantum-classical markov chain monte carlo

Abstract

A system and a method of sampling from a probability distribution approximating a Boltzmann distribution of an n-spin Ising model includes receiving, by a classical computer, coupling coefficients for spin-spin interactions, field coefficients local to each spin, and a temperature for the n-spin Ising model; selecting a first n-spin configuration; preparing a first n-qubit state on a quantum computer associated with the first n-spin configuration; applying a unitary operator to the first n-qubit state resulting in a second n-qubit state; measuring the second n-qubit state to identify a corresponding second n-spin configuration; calculating, on the classical computer, an acceptance probability to determine whether to replace the first n-spin configuration with the second n-spin configuration or to keep the first n-spin configuration to obtain an output n-spin configuration; and repeating the preparing, applying, measuring and calculating until the output n-spin configuration is sufficiently close to the Boltzmann distribution.