Magic State Injection on IBM Quantum Processors Above the Distillation Threshold

Magic State Injection on IBM Quantum Processors Above the Distillation Threshold | 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 Magic State Injection on IBM Quantum Processors Above the Distillation Threshold Younghun Kim, Martin Sevior, Muhammad Usman This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8303387/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 26 Feb, 2026 Read the published version in Scientific Reports → Version 1 posted 13 You are reading this latest preprint version Abstract The surface code family is a promising approach to implementing fault-tolerant quantum computations. Universal fault-tolerance requires error-corrected non-Clifford operations, in addition to Clifford gates, and for the former, it is imperative to experimentally demonstrate additional resources known as magic states. Another challenge is to efficiently embed surface codes into quantum hardware with connectivity constraints. This work simultaneously addresses both challenges by employing a qubit-efficient rotated heavy-hexagonal surface code for IBM quantum processors (\texttt{ibm_fez}) and implementing the magic state injection protocol. Our work reports error thresholds for both logical bit- and phase-flip errors, of $\approx0.37%$ and $\approx0.31%$, respectively, which are higher than the threshold values previously reported with traditional embedding. The post-selection-based preparation of logical magic states $|H_L\rangle$ and $|T_L\rangle$ achieve fidelities of $0.8806\pm0.0002$ and $0.8665\pm0.0003$, respectively, which are both above the magic state distillation threshold. The post-selection process yields an average success rate of $36.28 \pm 0.09%$. Additionally, we report the minimum fidelity among injected arbitrary single logical qubit states as $0.8356\pm0.0003$. Our work demonstrates the potential for realising non-Clifford logical gates by producing high-fidelity logical magic states on IBM quantum devices. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Supplementary Files Supplementary.zip Cite Share Download PDF Status: Published Journal Publication published 26 Feb, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 26 Dec, 2025 Reviews received at journal 24 Dec, 2025 Reviews received at journal 18 Dec, 2025 Reviewers agreed at journal 15 Dec, 2025 Reviews received at journal 14 Dec, 2025 Reviewers agreed at journal 13 Dec, 2025 Reviewers agreed at journal 12 Dec, 2025 Reviewers agreed at journal 12 Dec, 2025 Reviewers invited by journal 12 Dec, 2025 Editor invited by journal 12 Dec, 2025 Editor assigned by journal 08 Dec, 2025 Submission checks completed at journal 08 Dec, 2025 First submitted to journal 07 Dec, 2025 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. 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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-8303387","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":561817150,"identity":"188be103-c9d9-40d3-9040-e484e8dda10f","order_by":0,"name":"Younghun Kim","email":"data:image/png;base64,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","orcid":"","institution":"University of Melbourne","correspondingAuthor":true,"prefix":"","firstName":"Younghun","middleName":"","lastName":"Kim","suffix":""},{"id":561817151,"identity":"14bef333-bd31-4780-a2db-4d5bde8b2259","order_by":1,"name":"Martin Sevior","email":"","orcid":"","institution":"University of Melbourne","correspondingAuthor":false,"prefix":"","firstName":"Martin","middleName":"","lastName":"Sevior","suffix":""},{"id":561817152,"identity":"6c8e6937-b8f6-4ec1-bdc9-22fd78c10208","order_by":2,"name":"Muhammad Usman","email":"","orcid":"","institution":"University of Melbourne","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Usman","suffix":""}],"badges":[],"createdAt":"2025-12-08 04:23:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8303387/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8303387/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-026-40381-1","type":"published","date":"2026-02-26T15:57:40+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":98478453,"identity":"b982814d-f343-4f68-aaf4-bee38731a73a","added_by":"auto","created_at":"2025-12-18 04:27:33","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5285,"visible":true,"origin":"","legend":"","description":"","filename":"fd532411bb7f44fc9c3dd278b5c528e5.json","url":"https://assets-eu.researchsquare.com/files/rs-8303387/v1/171748d2773be5888251031b.json"},{"id":103765595,"identity":"72ac80e2-bfb7-40b1-ad98-a70bd4deac26","added_by":"auto","created_at":"2026-03-02 16:05:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":608549,"visible":true,"origin":"","legend":"","description":"","filename":"Main.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8303387/v1_covered_cf26d437-81bb-44a6-986f-068200e92487.pdf"},{"id":98478455,"identity":"207e5c7a-50a6-43b9-afe3-323e123b07e0","added_by":"auto","created_at":"2025-12-18 04:27:33","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":2950548,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementary.zip","url":"https://assets-eu.researchsquare.com/files/rs-8303387/v1/935cdef29821cb415f46ced4.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"Magic State Injection on IBM Quantum Processors Above the Distillation Threshold","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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8303387/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8303387/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The surface code family is a promising approach to implementing fault-tolerant quantum computations. Universal fault-tolerance requires error-corrected non-Clifford operations, in addition to Clifford gates, and for the former, it is imperative to experimentally demonstrate additional resources known as magic states. Another challenge is to efficiently embed surface codes into quantum hardware with connectivity constraints. This work simultaneously addresses both challenges by employing a qubit-efficient rotated heavy-hexagonal surface code for IBM quantum processors (\\texttt{ibm\\_fez}) and implementing the magic state injection protocol. Our work reports error thresholds for both logical bit- and phase-flip errors, of $\\approx0.37\\%$ and $\\approx0.31\\%$, respectively, which are higher than the threshold values previously reported with traditional embedding. The post-selection-based preparation of logical magic states $|H_L\\rangle$ and $|T_L\\rangle$ achieve fidelities of $0.8806\\pm0.0002$ and $0.8665\\pm0.0003$, respectively, which are both above the magic state distillation threshold. The post-selection process yields an average success rate of $36.28 \\pm 0.09\\%$. Additionally, we report the minimum fidelity among injected arbitrary single logical qubit states as $0.8356\\pm0.0003$. Our work demonstrates the potential for realising non-Clifford logical gates by producing high-fidelity logical magic states on IBM quantum devices.","manuscriptTitle":"Magic State Injection on IBM Quantum Processors Above the Distillation Threshold","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-18 04:27:25","doi":"10.21203/rs.3.rs-8303387/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-26T06:22:42+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-24T08:05:37+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-18T18:31:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"288201759313361706006098459777109360992","date":"2025-12-15T07:56:29+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-14T12:22:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"87836305034441968417306825762055094696","date":"2025-12-13T15:22:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"307062143317709720753491410152533091500","date":"2025-12-12T17:37:30+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"95238799444607951462809578395060548899","date":"2025-12-12T15:25:47+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-12T14:13:17+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-12-12T12:16:56+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-09T04:56:20+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-09T04:54:01+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-12-08T04:08:42+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"9ec13361-ca36-4e5d-ac83-47275f2ae94a","owner":[],"postedDate":"December 18th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":59824075,"name":"Physical sciences/Engineering"},{"id":59824076,"name":"Physical sciences/Mathematics and computing"},{"id":59824077,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-03-02T16:02:01+00:00","versionOfRecord":{"articleIdentity":"rs-8303387","link":"https://doi.org/10.1038/s41598-026-40381-1","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-02-26 15:57:40","publishedOnDateReadable":"February 26th, 2026"},"versionCreatedAt":"2025-12-18 04:27:25","video":"","vorDoi":"10.1038/s41598-026-40381-1","vorDoiUrl":"https://doi.org/10.1038/s41598-026-40381-1","workflowStages":[]},"version":"v1","identity":"rs-8303387","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8303387","identity":"rs-8303387","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}