Methods for non-variational heuristic quantum optimisation

TL;DR

This paper introduces non-variational quantum heuristics, QeSA and QePT, based on MCMC techniques, demonstrating superior scaling on complex problems and robustness to noise, offering a promising approach for near-term quantum optimization.

Contribution

It presents a novel non-variational hybrid quantum-classical approach using MCMC techniques, expanding the toolkit for quantum optimization beyond variational methods.

Findings

QeSA and QePT outperform classical benchmarks on hard problems.

Algorithms show inherent noise robustness.

Support parallel execution with classical communication.

Abstract

Optimisation plays a central role in a wide range of scientific and industrial applications, and quantum computing has been widely proposed as a means to achieve computational advantages in this domain. To date, research into the design of noise-resilient quantum algorithms has been dominated by variational approaches, while alternatives remain relatively unexplored. In this work, we introduce a novel class of quantum optimisation heuristics that forgo this variational framework in favour of a hybrid quantum-classical approach built upon Markov Chain Monte Carlo (MCMC) techniques. We introduce Quantum-enhanced Simulated Annealing (QeSA) and Quantum-enhanced Parallel Tempering (QePT), before validating these heuristics on hard Sherrington-Kirkpatrick instances and demonstrate their superior scaling over classical benchmarks. These algorithms are expected to exhibit inherent robustness to noise and support parallel execution across both quantum and classical resources with only classical communication required. As such, they offer a scalable and potentially competitive route toward solving large-scale optimisation problems with near-term quantum devices.