Quantum Error Correction by Purification

Quantum Error Correction by Purification | 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PDF Article Quantum Error Correction by Purification Jonathan Raghoonanan, Tim Byrnes This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9119304/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract We present a general-purpose quantum error correction primitive based on state purification via the SWAP test, which we refer to as purification quantum error correction (PQEC). This method operates on N noisy copies, requires minimally O(Mlog 2 N) data qubits to process the M-qubit inputs. In a similar way to standard QEC, the purification steps may be interleaved within a quantum algorithm to suppress the logical error rate. No postselection is performed and no knowledge of the state is required. We analyze its performance under a variety of error channels and find that PQEC is highly effective at boosting fidelity and reducing logical error rates, particularly for the depolarizing channel. Error thresholds for the local depolarizing channel are found to be 75% for any register size. For local dephasing, the error threshold is reduced to 50% but may be boosted using twirling. Physical sciences/Physics/Quantum physics/Quantum information Physical sciences/Physics/Quantum physics/Quantum simulation Physical sciences/Physics/Quantum physics/Qubits Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Under Review 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-9119304","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":613229421,"identity":"215d8487-afe6-4f5e-94d6-f2e2c62dbd9a","order_by":0,"name":"Jonathan Raghoonanan","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-6912-7443","institution":"New York University Shanghai","correspondingAuthor":true,"prefix":"","firstName":"Jonathan","middleName":"","lastName":"Raghoonanan","suffix":""},{"id":613229422,"identity":"643734d5-e028-440e-b826-69191e59edb5","order_by":1,"name":"Tim Byrnes","email":"","orcid":"","institution":"New York University Shanghai","correspondingAuthor":false,"prefix":"","firstName":"Tim","middleName":"","lastName":"Byrnes","suffix":""}],"badges":[],"createdAt":"2026-03-14 03:50:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9119304/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9119304/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105729075,"identity":"a249fb49-9b47-4ce6-9871-cae9522c57cd","added_by":"auto","created_at":"2026-03-30 11:13:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":964601,"visible":true,"origin":"","legend":"Article File","description":"","filename":"PurificationforErrorCorrection.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9119304/v1_covered_4c3873f3-b2bf-40ee-a038-6abf4d542f33.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Quantum Error Correction by Purification","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9119304/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9119304/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We present a general-purpose quantum error correction primitive based on state purification via the SWAP test, which we refer to as \u003ci\u003epurification quantum error correction\u003c/i\u003e (PQEC). 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