Simulation of Frustrated Ising Spins Using Three Coupled Parametric Oscillators: A Ground State Energy Approach

Simulation of Frustrated Ising Spins Using Three Coupled Parametric Oscillators: A Ground State Energy Approach | 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 Simulation of Frustrated Ising Spins Using Three Coupled Parametric Oscillators: A Ground State Energy Approach Chengxiao HAN, Yingming YAN This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9211211/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Frustrated Ising models play a fundamental role in understanding complex magnetic phenomena and are directly relevant to quantum annealing applications. However, determining the ground state energies of these systems remains computationally challenging due to the NP-hard nature of the problem. In this study, we propose and demonstrate a novel approach using a network of three coupled parametric oscillators to simulate frustrated Ising spins. By establishing a mapping between oscillator amplitudes, spin states, coupling constants with interaction strengths, and noise power, we show that the steady-state amplitude distribution of the oscillators corresponds to the ground state spin configuration. Numerical simulations for various coupling strengths successfully reproduce the ground state energies for triangular frustrated lattice systems. Our simulations reveal the existence of degenerate ground states that satisfy local energy minima for the frustrated Ising spin models. Our results suggest that coupled parametric oscillator networks may provide a viable physical implementation for studying frustrated Ising spins, with potential applications in quantum annealing and combinatorial optimization. Our work opens new avenues for exploring analog computing approaches to NP-hard optimization problems. Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Supplementary Files supplementarymaterials.pdf Cite Share Download PDF Status: Posted 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. 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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-9211211","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":623991341,"identity":"500abac7-1051-4125-928f-202c031eded9","order_by":0,"name":"Chengxiao HAN","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYBACfvaGxAcSFWxQLhtexRAg2XPgsYHFGVK0GNxIfCZQ2QbjEqXlQHIaw815fPbyM5IfMHwoO8zAP7uBgMMOHEt7OHMbW+KGG2kGjDPOHWaQuHMAvxa+gz3pxpLb2BIMeM4wMPO2HWYwkEgg4LLD/N+k/85hs5fvAWr5S4wWgWMMaRKSDWyMDcd7GJgZidEi2cOQbCBxDOiX420GB3vOpfNI3CCghV/+ATAqa47ZyzczP3zwo8xajn8GIb9AwDEweQCIeYhSDwQ1xCocBaNgFIyCkQgAnZxEjCXC44UAAAAASUVORK5CYII=","orcid":"","institution":"Suzhou Polytechnic University","correspondingAuthor":true,"prefix":"","firstName":"Chengxiao","middleName":"","lastName":"HAN","suffix":""},{"id":623991342,"identity":"cad74f4f-3466-4722-a496-4b9a2fb2f29f","order_by":1,"name":"Yingming YAN","email":"","orcid":"","institution":"Hong Kong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Yingming","middleName":"","lastName":"YAN","suffix":""}],"badges":[],"createdAt":"2026-03-24 11:24:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9211211/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9211211/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108182084,"identity":"8a14ff8a-da0b-412e-a50b-f0b8a006fba1","added_by":"auto","created_at":"2026-04-30 08:59:07","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1923583,"visible":true,"origin":"","legend":"","description":"","filename":"InvestigatingFrustratedIsingSpinsthroughSimulationofThreeCoupledParametricOscillatorsrevisedv2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9211211/v1_covered_47b7eaed-1b60-4bf8-9cb6-5971f8476d37.pdf"},{"id":107184199,"identity":"15446248-9350-45c0-b37b-c140becd220e","added_by":"auto","created_at":"2026-04-17 18:24:33","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":162595,"visible":true,"origin":"","legend":"","description":"","filename":"supplementarymaterials.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9211211/v1/00e0679059b4a2de456e81ac.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Simulation of Frustrated Ising Spins Using Three Coupled Parametric Oscillators: A Ground State Energy Approach","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9211211/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9211211/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFrustrated Ising models play a fundamental role in understanding complex magnetic phenomena and are directly relevant to quantum annealing applications. 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