Quantum-enhanced Markov Chain Monte Carlo for Combinatorial Optimization

TL;DR

This paper introduces a quantum-enhanced Markov chain Monte Carlo algorithm that effectively solves combinatorial optimization problems, demonstrating empirical success on IBM quantum hardware with promising scaling advantages.

Contribution

It presents a novel quantum-assisted sampling method combining warm-starting and parallel tempering for combinatorial optimization, showing practical results on the Maximum Independent Set problem.

Findings

Successfully recovered global optima for MIS instances up to 117 variables.

Demonstrated early evidence of a scaling advantage over classical methods.

Achieved results on IBM quantum hardware with 117 qubits.

Abstract

Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales known to be hard for state-of-the-art classical solvers is not yet in reach. In this work, we offer a different way to approach combinatorial optimization with near-term quantum computing. Motivated by the promising results observed in using quantum-enhanced Markov chain Monte Carlo (QeMCMC) for approximating complicated probability distributions, we combine ideas of sampling from the device with QeMCMC together with warm-starting and parallel tempering, in the context of combinatorial optimization. We demonstrate empirically that our algorithm recovers the global optima for instances of the Maximum Independent Set problem (MIS) up to 117 decision variables using 117 qubits on IBM quantum hardware. We show early evidence of a scaling advantage of our algorithm compared to similar classical methods for the chosen instances of MIS. MIS is practically relevant across domains like financial services and molecular biology, and, in some cases, already difficult to solve to optimality classically with only a few hundred decision variables.