The Riemann Hypothesis Emerges in Dynamical Quantum Phase Transitions

The Riemann Hypothesis Emerges in Dynamical Quantum Phase Transitions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article The Riemann Hypothesis Emerges in Dynamical Quantum Phase Transitions Shijie Wei, Yue Zhai, Quanfeng Lu, Wentao Yang, Pan Gao, Chao Wei, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8136886/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract The Riemann Hypothesis (RH), one of the most profound unsolved problems in mathematics, concerns the nontrivial zeros of the Riemann zeta function. Linking these zeros to physical phenomena offers new perspectives on their origin and verification. Here we establish a direct correspondence between these zeros and dynamical quantum phase transitions in two quantum many-body systems, characterized by the average accumulated phase factor and the Loschmidt amplitude respectively. This precise correspondence recasts the RH as the emergence of phase transitions at a unique temperature and identifies it as a previously unknown transition mechanism. We demonstrate this correspondence in a proof-of-principle experiment on a quantum processor. Moreover, we propose a quantum computational framework that implements both systems with polynomial resources, suggesting quantum advantage in probing the hypothesis. Our work bridges nonequilibrium quantum dynamics and number theory, positioning quantum computing as a powerful platform for exploring mathematical conjectures, phase transitions and beyond. Physical sciences/Physics/Quantum physics/Quantum simulation Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena Physical sciences/Mathematics and computing/Applied mathematics Full Text Additional Declarations There is NO Competing Interest. Supplementary Files Supplementnc.pdf Supplementary information for "The Riemann Hypothesis Emerges in Dynamical Quantum Phase Transitions" Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8136886","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":567763065,"identity":"2c34b65c-74ca-4b32-9174-ff42c4766519","order_by":0,"name":"Shijie 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