Quantum-enhanced Markov chain Monte Carlo

TL;DR

This paper introduces a quantum algorithm for Markov chain Monte Carlo sampling of classical Ising models, demonstrating faster convergence than classical methods on relevant problems, and implemented on a superconducting quantum processor.

Contribution

The paper presents a novel quantum MCMC algorithm that efficiently samples from Boltzmann distributions and is experimentally validated on a superconducting quantum processor.

Findings

Quantum MCMC converges faster than classical methods on certain problems.

The algorithm is successfully implemented on a superconducting quantum processor.

It opens pathways for quantum computers to solve practical sampling problems.

Abstract

Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from complicated distributions that are hard to sample from classically, but which seldom arise in applications. Here we introduce a quantum algorithm to sample from distributions that pose a bottleneck in several applications, which we implement on a superconducting quantum processor. The algorithm performs Markov chain Monte Carlo (MCMC), a popular iterative sampling technique, to sample from the Boltzmann distribution of classical Ising models. In each step, the quantum processor explores the model in superposition to propose a random move, which is then accepted or rejected by a classical computer and returned to the quantum processor, ensuring convergence to the desired Boltzmann distribution. We find that this quantum algorithm converges in fewer iterations than common classical MCMC alternatives on relevant problem instances, both in simulations and experiments. It therefore opens a new path for quantum computers to solve useful--not merely difficult--problems in the near term.