A rigorous quasipolynomial-time classical algorithm for SYK thermal expectations
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Quantum Physics arXiv:2604.21089 (quant-ph) [Submitted on 22 Apr 2026] Title:A rigorous quasipolynomial-time classical algorithm for SYK thermal expectations Authors:Alexander Zlokapa View a PDF of the paper titled A rigorous quasipolynomial-time classical algorithm for SYK thermal expectations, by Alexander Zlokapa View PDF HTML (experimental) Abstract:Estimating local observables in Gibbs states is a central problem in quantum simulation. While this task is BQP-complete at asymptotically low temperatures, the possibility of quantum advantage at constant temperature remains open. The Sachdev-Ye-Kitaev (SYK) model is a natural candidate: at any constant temperature, its Gibbs states have polynomial quantum circuit complexity and are not described by Gaussian states. Rigorous analyses of the SYK model are difficult due to the failure of known techniques using random matrix theory, cluster expansions, and rigorous formulations of the quantum path integral and replica trick. Despite this, we give a rigorous proof of a quasipolynomial-time classical algorithm that estimates SYK local thermal expectations at sufficiently high constant temperature. Our result introduces a new Wick-pair cluster expansion that we expect to be broadly useful for disordered quantum many-body systems. Comments: Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Data Structures and Algorithms (cs.DS); Mathematical Physics (math-ph) Cite as: arXiv:2604.21089 [quant-ph] (or arXiv:2604.21089v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.21089 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alexander Zlokapa [view email] [v1] Wed, 22 Apr 2026 21:14:04 UTC (49 KB) Full-text links: Access Paper: View a PDF of the paper titled A rigorous quasipolynomial-time classical algorithm for SYK thermal expectations, by Alexander ZlokapaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cond-mat cond-mat.dis-nn cs cs.DS math math-ph math.MP 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?)