Programmable Optical Differential Ising Machines for Phase Transition Simulation

Programmable Optical Differential Ising Machines for Phase Transition Simulation | 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 Programmable Optical Differential Ising Machines for Phase Transition Simulation Wenjia Zhang, Xin Ye, Jinmin Yang, Zuyuan He This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7651733/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 Drawing inspiration from the physical Ising model, optical Ising machines have emerged as a promising paradigm in optical computing. These machines typically utilize optical phase or amplitude modulators to represent the analog spin variables, which determine the final Hamiltonian by the combinatorial configuration of the complex optical field. However, current optical modulators exhibit relatively low modulation resolution and significant technical challenges arise when scaling up optical Ising systems to maintain consistent performance across integrated device clusters. Here we propose a programmable optical differential Ising machine that provides direct access to changes in the Hamiltonian. This system streamlines unnecessary matrix calculations, thereby reducing the requirements for the size and precision of the modulator matrix. Through numerical simulations on 60 to 100 spin MaxCut benchmark problems, we determine that the minimum required resolutions for the DAC and ADC are 6 bits and 5 bits, respectively, along with a significant tolerance of 0.3 rad for phase errors and over 10 multiplexing operations. Additionally, 100-spin experiments with a dual-channel system demonstrate its potential for phase transition simulation and solving complex optimization challenges. Physical sciences/Optics and photonics/Applied optics/Fibre optics and optical communications Physical sciences/Mathematics and computing/Computational science Full Text Additional Declarations There is NO Competing Interest. Supplementary Files ODINCPSupplement.pdf Programmable Optical Differential Ising Machines for Phase Transition Simulation 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-7651733","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":518832829,"identity":"dbdccf92-daf4-4707-af9d-847f1e80d4e9","order_by":0,"name":"Wenjia Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDElEQVRIie2RMUsDMRTHXzl4LqFdU/wSTwLR0tL7KnccOF2L4NKhSEE4F+us4IeJFK7LadeAgxVHb7ipdDjEpNYxR0fB/CDhT3g/XuAP4PH8USiyl00V4O6FH6y07gH5QcqPZ07A9tONCi3n6mI9hfD06HnxOajbV6SCp1cGw7FTKV4iinIIerfj8/4oQ04Kkz6D5NKlSJ0SRQhIKpViNLMKk8cMVDxzKW+lUb6A0aqU4qy2SmfTrGhGFGfASafiA3C3BRuVsDAfi+84kS5la55h92GBovdIiVPp3hTyZLsZhLRKRbWt8057ef2uy8nQqRiQ9kXYGnPTjs3knjcE699QAUwbRz0ej+d/8g1r81EUQxlhVAAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-9545-1124","institution":"Shanghai Jiao Tong University","correspondingAuthor":true,"prefix":"","firstName":"Wenjia","middleName":"","lastName":"Zhang","suffix":""},{"id":518832830,"identity":"41195a53-673d-4524-bde1-844f105bab67","order_by":1,"name":"Xin Ye","email":"","orcid":"https://orcid.org/0000-0001-6842-3526","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Xin","middleName":"","lastName":"Ye","suffix":""},{"id":518832831,"identity":"770a38a0-e027-4834-9d09-12c5e676a019","order_by":2,"name":"Jinmin Yang","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Jinmin","middleName":"","lastName":"Yang","suffix":""},{"id":518832832,"identity":"69b08655-9c0a-404b-b76c-93ba90a88e90","order_by":3,"name":"Zuyuan He","email":"","orcid":"https://orcid.org/0000-0002-7499-834X","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Zuyuan","middleName":"","lastName":"He","suffix":""}],"badges":[],"createdAt":"2025-09-18 16:45:34","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7651733/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7651733/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":92690229,"identity":"566cafea-cfeb-490a-8093-cf924f381ca2","added_by":"auto","created_at":"2025-10-03 04:40:36","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":10791609,"visible":true,"origin":"","legend":"","description":"","filename":"ODINCP4.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7651733/v1/8b67f6de56a19782c5140cfc.pdf"},{"id":92690227,"identity":"301583c7-3d8e-439e-a379-755683a783c6","added_by":"auto","created_at":"2025-10-03 04:40:36","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5543,"visible":true,"origin":"","legend":"","description":"","filename":"COMMSPHYS251556.json","url":"https://assets-eu.researchsquare.com/files/rs-7651733/v1/a0bf6788f5ff4b4623d27f54.json"},{"id":92690230,"identity":"97d29400-9b76-4945-abd1-2df4b1320018","added_by":"auto","created_at":"2025-10-03 04:40:36","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5319544,"visible":true,"origin":"","legend":"","description":"","filename":"ODINCPSupplement.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7651733/v1/b3d6c8df9d554d3e53d095ea.pdf"},{"id":94985265,"identity":"2c770938-1154-4169-8708-c343d3a82e69","added_by":"auto","created_at":"2025-11-03 06:57:49","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10868742,"visible":true,"origin":"","legend":"Article File","description":"","filename":"ODINCP4.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7651733/v1_covered_4179fdf1-ed76-4777-bb31-81d6a73a5fe2.pdf"},{"id":92690228,"identity":"b30b12f6-bf68-4311-9a32-c622911109e4","added_by":"auto","created_at":"2025-10-03 04:40:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":5319544,"visible":true,"origin":"","legend":"Programmable Optical Differential Ising Machines for Phase Transition Simulation","description":"","filename":"ODINCPSupplement.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7651733/v1/c0e74e924f5592f5e991daad.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Programmable Optical Differential Ising Machines for Phase Transition Simulation","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-7651733/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7651733/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Drawing inspiration from the physical Ising model, optical Ising machines have emerged as a promising paradigm in optical computing. These machines typically utilize optical phase or amplitude modulators to represent the analog spin variables, which determine the final Hamiltonian by the combinatorial configuration of the complex optical field. However, current optical modulators exhibit relatively low modulation resolution and significant technical challenges arise when scaling up optical Ising systems to maintain consistent performance across integrated device clusters.\r\nHere we propose a programmable optical differential Ising machine that provides direct access to changes in the Hamiltonian. \r\nThis system streamlines unnecessary matrix calculations, thereby reducing the requirements for the size and precision of the modulator matrix. Through numerical simulations on 60 to 100 spin MaxCut benchmark problems, we determine that the minimum required resolutions for the DAC and ADC are 6 bits and 5 bits, respectively, along with a significant tolerance of 0.3 rad for phase errors and over 10 multiplexing operations. Additionally, 100-spin experiments with a dual-channel system demonstrate its potential for phase transition simulation and solving complex optimization challenges.","manuscriptTitle":"Programmable Optical Differential Ising Machines for Phase Transition Simulation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-03 04:40:31","doi":"10.21203/rs.3.rs-7651733/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":"f2417412-d1da-4afd-aa45-c220d2cbcd5c","owner":[],"postedDate":"October 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":55133073,"name":"Physical sciences/Optics and photonics/Applied optics/Fibre optics and optical communications"},{"id":55133074,"name":"Physical sciences/Mathematics and computing/Computational science"}],"tags":[],"updatedAt":"2026-03-27T14:12:29+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-03 04:40:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7651733","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7651733","identity":"rs-7651733","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}