Syndrome decoding by quantum approximate optimization

Syndrome decoding by quantum approximate 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 Syndrome decoding by quantum approximate optimization Ching-Yi Lai, Kao-Yueh Kuo, Bo-Jyun Liao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4118956/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Nov, 2024 Read the published version in Quantum Information Processing → Version 1 posted 7 You are reading this latest preprint version Abstract The syndrome decoding problem is known to be NP-complete. The goal of the decoder is to find an error of low weight that corresponds to a given syndrome obtained from a parity-check matrix. We use the quantum approximate optimization algorithm (QAOA) to address the syndrome decoding problem with elegantly-designed reward Hamiltonians based on both generator and check matrices for classical and quantum codes.We evaluate the level-4 check-based QAOA decoding of the [7,4,3] Hamming code, as well as the level-4 generator-based QAOA decoding of the [[5,1,3]] quantum code.Remarkably, the simulation results demonstrate that the decoding performances match those of the maximum likelihood decoding. Moreover, we explore the possibility of enhancing QAOA by introducing additional redundant clauses to a combinatorial optimization problem while keeping the number of qubits unchanged. Finally, we study QAOA decoding of degenerate quantum codes.Typically, conventional decoders aim to find a unique error of minimum weight that matches a given syndrome. However, our observations reveal that QAOA has the intriguing ability to identify degenerate errors of comparable weight, providing multiple potential solutions that match the given syndrome with comparable probabilities.This is illustrated through simulations of the generator-based QAOA decoding of the [[9,1,3]] Shor code on specific error syndromes. degeneracy QAOA quantum check-based decoding quantum generator-base decoding Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 01 Nov, 2024 Read the published version in Quantum Information Processing → Version 1 posted Editorial decision: Revision requested 27 Jun, 2024 Reviews received at journal 12 Jun, 2024 Reviewers agreed at journal 18 May, 2024 Reviewers invited by journal 03 Apr, 2024 Submission checks completed at journal 17 Mar, 2024 Editor assigned by journal 17 Mar, 2024 First submitted to journal 17 Mar, 2024 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-4118956","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":280646604,"identity":"1a961031-4e83-4d18-8607-5f0b88624af7","order_by":0,"name":"Ching-Yi Lai","email":"","orcid":"","institution":"National Yang Ming Chiao Tung University","correspondingAuthor":false,"prefix":"","firstName":"Ching-Yi","middleName":"","lastName":"Lai","suffix":""},{"id":280646605,"identity":"934d1dfb-3313-4df9-9d16-910ddac76202","order_by":1,"name":"Kao-Yueh Kuo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYBACCSBmbGBgkANxDjwgRYsxWEsCKVoSG0A8orRIzsgxk5zZZpM+P+zwQ6AtdnK6DQS0SEsAtWxsS8vdeDvNAKgl2djsAAEtchK52yQfth3O3Tg7AaTlQOI2YrWkG85O/0CcFmmQlo1thxPkpXOItEWy5/1nyxnn0gw3SOcUHEgwIMIvEsfTEm/2lNnIy89O3/zhQ4WdHEEtDAIJENoArNKAkHIQ4IcaKt9AjOpRMApGwSgYkQAAFVpHO9bGac0AAAAASUVORK5CYII=","orcid":"","institution":"National Yang Ming Chiao Tung University","correspondingAuthor":true,"prefix":"","firstName":"Kao-Yueh","middleName":"","lastName":"Kuo","suffix":""},{"id":280646606,"identity":"21ead90b-369c-4340-845a-89d56e223d25","order_by":2,"name":"Bo-Jyun Liao","email":"","orcid":"","institution":"National Yang Ming Chiao Tung University","correspondingAuthor":false,"prefix":"","firstName":"Bo-Jyun","middleName":"","lastName":"Liao","suffix":""}],"badges":[],"createdAt":"2024-03-17 23:14:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4118956/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4118956/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11128-024-04568-7","type":"published","date":"2024-11-01T16:13:10+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":68206968,"identity":"a4c0280d-c376-4a4a-9e58-9abd677ecef6","added_by":"auto","created_at":"2024-11-04 16:34:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1900593,"visible":true,"origin":"","legend":"","description":"","filename":"QAOAdec20240317qinptosubmitupload.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4118956/v1_covered_5a672ec9-160e-40e3-9b31-44ae6020721f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Syndrome decoding by quantum approximate optimization","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"degeneracy, QAOA, quantum check-based decoding, quantum generator-base decoding","lastPublishedDoi":"10.21203/rs.3.rs-4118956/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4118956/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The syndrome decoding problem is known to be NP-complete. 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