Quantum-enhanced Markov Chain Monte Carlo for Combinatorial Optimization
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Quantum Physics arXiv:2602.06171 (quant-ph) [Submitted on 5 Feb 2026] Title:Quantum-enhanced Markov Chain Monte Carlo for Combinatorial Optimization Authors:Kate V. Marshall, Daniel J. Egger, Michael Garn, Francesca Schiavello, Sebastian Brandhofer, Christa Zoufal, Stefan Woerner View a PDF of the paper titled Quantum-enhanced Markov Chain Monte Carlo for Combinatorial Optimization, by Kate V. Marshall and 6 other authors View PDF HTML (experimental) 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. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.06171 [quant-ph] (or arXiv:2602.06171v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.06171 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Kate Marshall [view email] [v1] Thu, 5 Feb 2026 20:20:54 UTC (14,181 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum-enhanced Markov Chain Monte Carlo for Combinatorial Optimization, by Kate V. Marshall and 6 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)