Practical advantage beyond the quadratic speedup limit with fully-quantum walks

Quantum Physics arXiv:2607.22818 (quant-ph) [Submitted on 24 Jul 2026] Title:Practical advantage beyond the quadratic speedup limit with fully-quantum walks Authors:Massimiliano Incudini, Guglielmo Mazzola View a PDF of the paper titled Practical advantage beyond the quadratic speedup limit with fully-quantum walks, by Massimiliano Incudini and 1 other authors View PDF Abstract:We introduce a new class of fully-quantum Metropolis walks in which both the proposal and acceptance steps are intrinsically quantum. Unlike standard quantum walks obtained by quantizing classically efficient Markov chains, our algorithm employs Hamiltonian simulation as a quantum-native proposal mechanism, enlarging the class of quantum walks beyond classical counterparts. We target the problem of sampling from the low-temperature Gibbs distribution of classical dense Ising models, within a fixed error in total variation distance. This approach achieves about a cubic polynomial asymptotic advantage over previous quantum-walks, resulting in a total sixth-degree polynomial queries speedup compared to the best classical walk. This shows that speedups beyond the widely assumed quadratic limit are possible within the quantum walk formalism. We perform a complete fault-tolerant compilation of all algorithmic primitives and benchmark against CPU, GPU, and FPGA implementations of the best classical Markov chain. Under identical hardware assumptions, the resulting advantage runtime crossover is reduced from approximately $10^3$ years for conventional quantum walks to less than one day. These results identify fully-quantum Markov chains as a promising route toward practical quantum advantage. Comments: Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG) Cite as: arXiv:2607.22818 [quant-ph] (or arXiv:2607.22818v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.22818 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Massimiliano Incudini [view email] [v1] Fri, 24 Jul 2026 18:00:06 UTC (1,324 KB) Full-text links: Access Paper: View a PDF of the paper titled Practical advantage beyond the quadratic speedup limit with fully-quantum walks, by Massimiliano Incudini and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: cond-mat cond-mat.dis-nn cs cs.LG 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?)