SYK thermal expectations are classically easy at any temperature
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Quantum Physics arXiv:2602.22619 (quant-ph) [Submitted on 26 Feb 2026] Title:SYK thermal expectations are classically easy at any temperature Authors:Alexander Zlokapa, Bobak T. Kiani View a PDF of the paper titled SYK thermal expectations are classically easy at any temperature, by Alexander Zlokapa and Bobak T. Kiani View PDF Abstract:Estimating thermal expectations of local observables is a natural target for quantum advantage. We give a simple classical algorithm that approximates thermal expectations, and we show it has quasi-polynomial cost $n^{O(\log n/\epsilon)}$ for all temperatures above a phase transition in the free energy. For many natural models, this coincides with the entire fast-mixing, quantumly easy phase. Our results apply to the Sachdev-Ye-Kitaev (SYK) model at any constant temperature -- including when the thermal state is highly entangled and satisfies polynomial quantum circuit lower bounds, a sign problem, and nontrivial instance-to-instance fluctuations. Our analysis of the SYK model relies on the replica trick to control the complex zeros of the partition function. Comments: Subjects: Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS) Cite as: arXiv:2602.22619 [quant-ph] (or arXiv:2602.22619v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.22619 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alexander Zlokapa [view email] [v1] Thu, 26 Feb 2026 04:48:32 UTC (824 KB) Full-text links: Access Paper: View a PDF of the paper titled SYK thermal expectations are classically easy at any temperature, by Alexander Zlokapa and Bobak T. KianiView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cs cs.DS 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?)