Quantum Markov chain Monte Carlo method with programmable quantum simulators

TL;DR

This paper introduces a quantum Markov chain Monte Carlo algorithm leveraging Many-Body Localized phases, enabling sampling from complex quantum distributions and solving optimization problems on programmable quantum simulators.

Contribution

It presents a novel quantum Markov chain method utilizing MBL phases for efficient sampling and optimization, adaptable to existing quantum hardware.

Findings

Demonstrates how MBL phases enable ergodicity and sampling from quantum state distributions.

Shows the algorithm can be implemented on quantum devices simulating Floquet dynamics.

Applies the method to solve combinatorial optimization problems of quadratic order and higher.

Abstract

In this work, we present a quantum Markov chain algorithm for many-body systems that utilizes a special phase of matter known as the Many-Body Localized (MBL) phase. We show how the properties of the MBL phase enable one to address the conditions for ergodicity and sampling from distributions of quantum states. We demonstrate how to exploit the thermalized-to-localized transition to tune the acceptance rate of the Markov chain, and apply the algorithm to solve a range of combinatorial optimization problems of quadratic order and higher. The algorithm can be implemented on any quantum processing unit capable of simulating the Floquet dynamics of a one-dimensional Ising chain with nearest-neighbor interactions, providing a practical way of sampling from thermal distributions of Hamiltonians that cannot be natively implemented on the quantum hardware.