Fully Connected Ising Machine with Fully Parallel Spin Updates Based on Discrete Field-Induced Bifurcation for Combinatorial Optimization

Fully Connected Ising Machine with Fully Parallel Spin Updates Based on Discrete Field-Induced Bifurcation for Combinatorial Optimization | 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 Research Article Fully Connected Ising Machine with Fully Parallel Spin Updates Based on Discrete Field-Induced Bifurcation for Combinatorial Optimization Yixuan Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7017550/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 Combinatorial optimization is fundamental to domains such as machine learning, logistics, and network design. However, many of these problems are NP-hard, posing a significant challenge to classical von Neumann architectures. As a promising alternative, Ising machines map these problems to spin systems and solve them by minimizing the Ising Hamiltonian. Fully connected Ising topologies are particularly desirable, as they enable direct and lossless problem mapping. Yet, most existing hardware implementations either suffer from limited connectivity or rely on complex mechanisms such as spin replication or differential equation solving, which hinder scalability and efficiency. In this work, we propose a novel Discrete Field-Induced Bifurcation (DFIB) method that enables fully parallel spin updates without spin duplication. Unlike simulated bifurcation approaches that require solving large differential systems, DFIB employs a simplified update rule based on multiply-accumulate (MAC) operations, enabling low-complexity, scalable hardware implementation. To further improve solution quality, a lightweight periodic random masking strategy is introduced to escape local minima. We also present a RRAM-based current-branching architecture for efficient local field computation, which supports high weight precision and mitigates current overload issues common in in-memory computing. Simulation results on 100-node fully connected Max-Cut problems show that DFIB achieves up to 98% of optimal solution quality, with time-to-solution ranging from 0.14us to 3.4us, depending on graph density. In dense graphs, convergence to 95% of the optimum is achieved within 10 iterations, even without perturbation. These results demonstrate DFIB’s superior speed, accuracy, and scalability for large-scale combinatorial optimization. Electrical Engineering Ising machine analog computing combinatorial optimization problem (COP) annealing processor Full Text Additional Declarations The authors declare no competing interests. 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7017550","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":478894658,"identity":"1238ce5f-cd34-458f-aebf-9ecdeb5f7052","order_by":0,"name":"Yixuan Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDElEQVRIie3RsUoDMRjA8RyB3PJp1xTh+gopBxE5bV+lR6BdpAhCyZhyEF+hgw9xk+CWEKFLcD7oorg6VAQnQWNXveNGh/zJFL4fgXwIxWL/sAFOlNmzcyAY2yeJ8OGWdpHhTbW2GznPjlMtmO9DmN9WDrzLM/Cc9iKoKZU50rjU9JJLq4vRKcJ2B2iybBPJJpChJoHMV43Vi/G9IqIAJK7bCKaBjDUEIu52b9oltQF+AsiUqoWQHxLmw5nxK6vdtDaDj04CYJUxnuUEHjgKpAyvkE5C07WySs4yEj6ZmseFqB3Jz26ZaCVTl768f7IvGFXY7s2quKi31XPzKiet5I8Oq2H952OxWCz2u2+LY2EBEXN5zwAAAABJRU5ErkJggg==","orcid":"","institution":"Fudan University","correspondingAuthor":true,"prefix":"","firstName":"Yixuan","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2025-07-01 07:56:09","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7017550/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7017550/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":85876870,"identity":"37a63784-4da8-41cc-b93c-5ddb0ae809d7","added_by":"auto","created_at":"2025-07-02 15:19:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2162584,"visible":true,"origin":"","legend":"","description":"","filename":"FullyConnectedIsingMachinewithFullyParallelSpinUpdatesBasedonDiscreteFieldInducedBifurcationforCombinatorialOptimization.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7017550/v1_covered_73234685-154e-432c-aca5-199174548643.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eFully Connected Ising Machine with Fully Parallel Spin Updates Based on Discrete Field-Induced Bifurcation for Combinatorial Optimization\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Ising machine, analog computing, combinatorial optimization problem (COP), annealing processor","lastPublishedDoi":"10.21203/rs.3.rs-7017550/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7017550/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCombinatorial optimization is fundamental to domains such as machine learning, logistics, and network design. However, many of these problems are NP-hard, posing a significant challenge to classical von Neumann architectures. As a promising alternative, Ising machines map these problems to spin systems and solve them by minimizing the Ising Hamiltonian. Fully connected Ising topologies are particularly desirable, as they enable direct and lossless problem mapping. Yet, most existing hardware implementations either suffer from limited connectivity or rely on complex mechanisms such as spin replication or differential equation solving, which hinder scalability and efficiency.\u003c/p\u003e\n\u003cp\u003e\t\u003c/p\u003e\n\u003cp\u003e\tIn this work, we propose a novel Discrete Field-Induced Bifurcation (DFIB) method that enables fully parallel spin updates without spin duplication. Unlike simulated bifurcation approaches that require solving large differential systems, DFIB employs a simplified update rule based on multiply-accumulate (MAC) operations, enabling low-complexity, scalable hardware implementation. To further improve solution quality, a lightweight periodic random masking strategy is introduced to escape local minima. We also present a RRAM-based current-branching architecture for efficient local field computation, which supports high weight precision and mitigates current overload issues common in in-memory computing.\u003c/p\u003e\n\u003cp\u003e\t\u003c/p\u003e\n\u003cp\u003e\tSimulation results on 100-node fully connected Max-Cut problems show that DFIB achieves up to 98% of optimal solution quality, with time-to-solution ranging from 0.14us to 3.4us, depending on graph density. In dense graphs, convergence to 95% of the optimum is achieved within 10 iterations, even without perturbation. These results demonstrate DFIB’s superior speed, accuracy, and scalability for large-scale combinatorial optimization.\u003c/p\u003e","manuscriptTitle":"Fully Connected Ising Machine with Fully Parallel Spin Updates Based on Discrete Field-Induced Bifurcation for Combinatorial Optimization","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-02 15:10:57","doi":"10.21203/rs.3.rs-7017550/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"8d16e6b3-c5f3-47da-9b37-37a9e858ee35","owner":[],"postedDate":"July 2nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":50845576,"name":"Electrical Engineering"}],"tags":[],"updatedAt":"2025-07-02T15:10:57+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-02 15:10:57","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7017550","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7017550","identity":"rs-7017550","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}