Speed-up via Quantum Sampling

TL;DR

This paper introduces a quantum algorithm that accelerates the process of sampling from Markov chains, offering faster convergence to stationary distributions and improvements over previous quantum methods.

Contribution

The paper presents a new quantum sampling algorithm that outperforms prior approaches in speed, enabling more efficient quantum sampling from Markov chains and classical Hamiltonian ground states.

Findings

Quantum algorithm achieves faster sampling from Markov chains.

Significant improvement over previous adiabatic-based quantum algorithms.

Provides a speed-up for obtaining ground states of classical Hamiltonians.

Abstract

The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether quantum computers can speed-up classical mixing processes based on Markov chains. To this end, we present a new quantum algorithm, making it possible to prepare a quantum sample, i.e., a coherent version of the stationary distribution of a reversible Markov chain. Our algorithm has a significantly better running time than that of a previous algorithm based on adiabatic state generation. We also show that our methods provide a speed-up over a recently proposed method for obtaining ground states of (classical) Hamiltonians.