Universal Bit-Flip Error Correction for Arbitrary-Size Data Registers Using a Single Ancilla Qubit via Similarity Propagation

Universal Bit-Flip Error Correction for Arbitrary-Size Data Registers Using a Single Ancilla Qubit via Similarity Propagation | 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 Universal Bit-Flip Error Correction for Arbitrary-Size Data Registers Using a Single Ancilla Qubit via Similarity Propagation Dimitrios Gryllakis, Kyriakos Sgarbas This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9076885/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 Quantum computing systems remain fragile due to decoherence and operational noise. Although large-scale quantum error correction offers robustness against general error models, its qubit and circuit overhead is often prohibitive for near-term devices. In this work, we present a scalable bit-flip error correction methodology that protects an arbitrary number of data qubits using only a single ancilla qubit, independent of register size. The method extends a previously introduced 4-qubit correction circuit for a 3-qubit data block and introduces a novel similarity circuit that enforces intra-triplet uniformity (always producing outputs of the form 000 or 111). Dedicated tail subcircuits handle the cases N = 3n + 1 and N = 3n + 2. Quantum error correction bit-flip error single ancilla scalable quantum circuits reversible logic Full Text Additional Declarations No competing interests reported. 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-9076885","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":605930163,"identity":"6e2cf5f0-d8c2-466d-893e-3087a08f3694","order_by":0,"name":"Dimitrios Gryllakis","email":"data:image/png;base64,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","orcid":"","institution":"University of Patras","correspondingAuthor":true,"prefix":"","firstName":"Dimitrios","middleName":"","lastName":"Gryllakis","suffix":""},{"id":605930168,"identity":"b8c668a2-ae8b-4b5a-a755-c06fe555477b","order_by":1,"name":"Kyriakos Sgarbas","email":"","orcid":"","institution":"University of Patras","correspondingAuthor":false,"prefix":"","firstName":"Kyriakos","middleName":"","lastName":"Sgarbas","suffix":""}],"badges":[],"createdAt":"2026-03-09 21:08:55","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9076885/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9076885/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108900152,"identity":"1278a1df-d9e6-48b9-80ae-dbdc8b635680","added_by":"auto","created_at":"2026-05-10 08:10:16","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":740209,"visible":true,"origin":"","legend":"","description":"","filename":"ErrorCorMultQUBITS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9076885/v1_covered_77f6245a-e168-4e77-be11-704e2900043e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Universal Bit-Flip Error Correction for Arbitrary-Size Data Registers Using a Single Ancilla Qubit via Similarity Propagation","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":"Quantum error correction, bit-flip error, single ancilla, scalable quantum circuits, reversible logic","lastPublishedDoi":"10.21203/rs.3.rs-9076885/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9076885/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eQuantum computing systems remain fragile due to decoherence and operational noise. 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