Optimal Penalty Weights for CQM-to-BQM Conversion]{Towards QPU-only Quantum Annealing: Optimal Penalty Weights for CQM-to-BQM Conversion

Optimal Penalty Weights for CQM-to-BQM Conversion]{Towards QPU-only Quantum Annealing: Optimal Penalty Weights for CQM-to-BQM Conversion | 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 Optimal Penalty Weights for CQM-to-BQM Conversion]{Towards QPU-only Quantum Annealing: Optimal Penalty Weights for CQM-to-BQM Conversion Junwhan Cho, Minjae Lee, Insung Kim, Dongjae Lee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8842888/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Quantum Annealing hardware, particularly D-Wave systems, requires problems to be formulated as Binary Quadratic Models (BQM). While hybrid solvers support Constrained Quadratic Models (CQM) with native constraint handling, Quantum Processing Unit-only execution remains an important research direction. CQMs can be transformed into BQMs by encoding constraints as penalty terms, with weights controlling the trade-off between optimization and constraint satisfaction. However, optimal penalty weight selection for general CQM-to-BQM transformation remains underexplored. This work investigates optimal penalty weights for such transformations. We focus on a restricted class of CQMs where constraints follow a specific structural form while the objective function remains general, and experimentally determine optimal weights using classical solvers. We present methods for encoding these constraints and conduct experiments to examine how optimal penalty weights vary with problem scale and constraint count. Through comprehensive analysis, we identify patterns and relationships that provide practical guidance for penalty weight selection. Quantum Annealing Binary Quadratic Model Constrained Quadratic Model Penalty Method Optimization Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 21 Apr, 2026 Reviewers agreed at journal 01 Apr, 2026 Reviewers agreed at journal 31 Mar, 2026 Reviewers invited by journal 30 Mar, 2026 Editor assigned by journal 12 Feb, 2026 Submission checks completed at journal 12 Feb, 2026 First submitted to journal 10 Feb, 2026 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-8842888","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":614308479,"identity":"69fd9a8f-bd87-45d5-9fd1-6b22f9d8cdb1","order_by":0,"name":"Junwhan Cho","email":"","orcid":"","institution":"Kangwon National University","correspondingAuthor":false,"prefix":"","firstName":"Junwhan","middleName":"","lastName":"Cho","suffix":""},{"id":614308480,"identity":"9996c6a8-f999-4589-9402-8a0a7901addd","order_by":1,"name":"Minjae Lee","email":"","orcid":"","institution":"Kangwon National University","correspondingAuthor":false,"prefix":"","firstName":"Minjae","middleName":"","lastName":"Lee","suffix":""},{"id":614308481,"identity":"57937ba4-aac4-466d-bf69-e23bf36df624","order_by":2,"name":"Insung Kim","email":"","orcid":"","institution":"Korea University","correspondingAuthor":false,"prefix":"","firstName":"Insung","middleName":"","lastName":"Kim","suffix":""},{"id":614308482,"identity":"fa1fe8ad-3a98-4116-94ae-a4a0caa10068","order_by":3,"name":"Dongjae Lee","email":"data:image/png;base64,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","orcid":"","institution":"Kangwon National University","correspondingAuthor":true,"prefix":"","firstName":"Dongjae","middleName":"","lastName":"Lee","suffix":""}],"badges":[],"createdAt":"2026-02-10 15:54:48","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8842888/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8842888/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106401520,"identity":"520ea0dd-0aa6-4b87-8d58-aadfbcab3c53","added_by":"auto","created_at":"2026-04-08 09:06:13","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3689453,"visible":true,"origin":"","legend":"","description":"","filename":"TowardsQPUOnly.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8842888/v1_covered_30975768-c599-4b66-90d7-c069d40177cf.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Optimal Penalty Weights for CQM-to-BQM Conversion]{Towards QPU-only Quantum Annealing: Optimal Penalty Weights for CQM-to-BQM Conversion","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"quantum-information-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qinp","sideBox":"Learn more about [Quantum Information Processing](http://link.springer.com/journal/11128)","snPcode":"11128","submissionUrl":"https://submission.nature.com/new-submission/11128/3","title":"Quantum Information Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Quantum Annealing, Binary Quadratic Model, Constrained Quadratic Model, Penalty Method, Optimization","lastPublishedDoi":"10.21203/rs.3.rs-8842888/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8842888/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Quantum Annealing hardware, particularly D-Wave systems, requires problems to be formulated as Binary Quadratic Models (BQM). 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