Quantum-stabilized patterns in a vector Hopfield network
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Quantum Physics arXiv:2606.06597 (quant-ph) [Submitted on 4 Jun 2026] Title:Quantum-stabilized patterns in a vector Hopfield network Authors:Richard D. Barney, Sharba Bhattacharjee, Victor Galitski, Kartiek Agarwal, Ivar Martin View a PDF of the paper titled Quantum-stabilized patterns in a vector Hopfield network, by Richard D. Barney and 4 other authors View PDF HTML (experimental) Abstract:We introduce the quantum vector Hopfield network, in which patterns are formed by orientations of quantum vector spins; quantum dynamics arise intrinsically from the non-commutativity of the spin operators. We derive the equations of state and the phase diagrams for this network as well as its classical counterpart. We find that quantum fluctuations, surprisingly, stabilize the stored patterns. Both the critical retrieval temperature and the target pattern overlap are enhanced relative to the classical network. Additionally, we find that this enhancement grows with pattern loading up to network capacity. We interpret this effect as an analog of quantum order-by-disorder, a mechanism by which quantum fluctuations promote the formation of ordered phases. These findings offer a new route to quantum-enhanced associative memory. Comments: Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2606.06597 [quant-ph] (or arXiv:2606.06597v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.06597 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Richard Barney [view email] [v1] Thu, 4 Jun 2026 18:00:06 UTC (412 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum-stabilized patterns in a vector Hopfield network, by Richard D. Barney and 4 other authorsView PDFHTML (experimental)TeX Source view license Ancillary-file links: Ancillary files (details): sup.tex sup_imgs/hist_K5_15.pdf Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.dis-nn cond-mat.stat-mech 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?)