Planar Fault-Tolerant Quantum Computation with Low Overhead

Planar Fault-Tolerant Quantum Computation with Low Overhead | 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 Planar Fault-Tolerant Quantum Computation with Low Overhead Yingli Yang, Guo Zhang, Ying Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7314616/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate bicycle (BB) codes, achieve dramatic reductions in qubit overhead, yet their logical operations remain a key challenge under planar hardware constraints. Here, we introduce code craft, a framework for designing fault-tolerant logical operations on planar BB codes within a translationally invariant, two-dimensional qubit lattice. By systematically deforming codes through local modifications---stretching, cutting, and painting---we enable the manipulation of logical qubits using strictly planar operations. We establish fault tolerance through numerical optimization of code distances and show that logical operations, including controlled-NOT gates, state transfers, and Pauli measurements, can be efficiently implemented within this framework to assemble an individually addressable logical qubit network. Universal quantum computation can then be realized by coupling just one BB-code logical qubit to a surface-code block. By combining the high encoding efficiency of qLDPC codes with geometric locality, our approach offers a practical and resource-efficient path to fault-tolerant quantum computation. Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Supplementary Files SupInf.pdf Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 14 Oct, 2025 Reviews received at journal 04 Oct, 2025 Reviews received at journal 24 Sep, 2025 Reviews received at journal 23 Sep, 2025 Reviewers agreed at journal 31 Aug, 2025 Reviewers agreed at journal 30 Aug, 2025 Reviewers agreed at journal 27 Aug, 2025 Reviewers invited by journal 25 Aug, 2025 Editor assigned by journal 15 Aug, 2025 Submission checks completed at journal 08 Aug, 2025 First submitted to journal 07 Aug, 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. 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-7314616","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":508205211,"identity":"fa05e3b6-f736-4d6b-abe2-d9b03b668deb","order_by":0,"name":"Yingli Yang","email":"","orcid":"","institution":"Graduate School of China Academy of Engineering Physics","correspondingAuthor":false,"prefix":"","firstName":"Yingli","middleName":"","lastName":"Yang","suffix":""},{"id":508205212,"identity":"62885672-263b-4337-b9c3-812a3a96c7f7","order_by":1,"name":"Guo Zhang","email":"","orcid":"","institution":"Graduate School of China Academy of Engineering Physics","correspondingAuthor":false,"prefix":"","firstName":"Guo","middleName":"","lastName":"Zhang","suffix":""},{"id":508205213,"identity":"24eb4c8a-51be-40f2-8026-90422a6c49ba","order_by":2,"name":"Ying Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVRIiWNgGAWjYDACdsbGByRqYWZsNiBVCwObBGk6DA4zt1V++WMnzy/dwPjhB4NdHhFaGNtuy7YlG86cc4BZsochuZg4LZINBxg33EhgkGZgOJDYQIyWYok/B+z330hg/k20FsYPbAcSN0gksBFni+RhxmZpxrbk5Bl3DrZZ9hgkE9bCd7z94ccff+xs+2c3H77xo8KOsBaFA8Co4QGxJBiBiomJVXmgOsYfYC1EqB4Fo2AUjIKRCQDoqT2/73VJgAAAAABJRU5ErkJggg==","orcid":"","institution":"Graduate School of China Academy of Engineering Physics","correspondingAuthor":true,"prefix":"","firstName":"Ying","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2025-08-07 04:38:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7314616/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7314616/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90442153,"identity":"3c6c105f-aece-4916-aa6f-5c412f388558","added_by":"auto","created_at":"2025-09-02 18:57:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":559830,"visible":true,"origin":"","legend":"","description":"","filename":"planarprotocol.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7314616/v1_covered_948d3a5f-47c9-434e-aaaa-367b3a5e084e.pdf"},{"id":90441528,"identity":"a1508f3c-d167-47ee-95fd-6d6ea938834e","added_by":"auto","created_at":"2025-09-02 18:49:40","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":204628,"visible":true,"origin":"","legend":"","description":"","filename":"SupInf.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7314616/v1/d0188d5503fdecfc3a0f3ee0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Planar Fault-Tolerant Quantum Computation with Low Overhead","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":"npj-quantum-information","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjqi","sideBox":"Learn more about [npj Quantum Information](http://www.nature.com/npjqi/)","snPcode":"41534","submissionUrl":"https://mts-npjqi.nature.com/","title":"npj Quantum Information","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7314616/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7314616/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. 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