Accelerating quantum Gibbs sampling without quantum walks
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Quantum Physics arXiv:2604.22996 (quant-ph) [Submitted on 24 Apr 2026] Title:Accelerating quantum Gibbs sampling without quantum walks Authors:Jiaqi Leng, Jiaqing Jiang, Lin Lin View a PDF of the paper titled Accelerating quantum Gibbs sampling without quantum walks, by Jiaqi Leng and 2 other authors View PDF HTML (experimental) Abstract:Szegedy's quantum walk gives a generic quadratic speedup for reversible classical Markov chains, but extending this mechanism to quantum Gibbs sampling has remained challenging beyond special cases. We present a walk-free quantum algorithm for preparing purified Gibbs states with a quadratic improvement in spectral-gap dependence for a broad class of quantum Gibbs samplers that satisfy exact Kubo-Martin-Schwinger detailed balance. Our main structural result is an explicit factorization of the corresponding parent Hamiltonian into noncommutative first-order operators. This turns purified Gibbs-state preparation into a singular-value filtering problem and enables a quantum singular value transformation algorithm with quadratically improved gap dependence under standard coherent-access assumptions. The framework applies to several efficiently implementable Gibbs samplers beyond the Davies setting. We also introduce an auxiliary dissipative dynamics based on the same factorization, which can be used to generate warm starts in the doubled Hilbert space in metastable regimes. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Numerical Analysis (math.NA) Cite as: arXiv:2604.22996 [quant-ph] (or arXiv:2604.22996v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.22996 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jiaqi Leng [view email] [v1] Fri, 24 Apr 2026 20:25:18 UTC (538 KB) Full-text links: Access Paper: View a PDF of the paper titled Accelerating quantum Gibbs sampling without quantum walks, by Jiaqi Leng and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cs cs.NA math math-ph math.MP math.NA 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?) 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?)