Fault-Tolerant Quantum Communication Systems Using Clifford Hierarchy-based CSS Codes

Fault-Tolerant Quantum Communication Systems Using Clifford Hierarchy-based CSS Codes | 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 Fault-Tolerant Quantum Communication Systems Using Clifford Hierarchy-based CSS Codes Mahendra Kumar Das, Payal Bhardwaj, Bishnu Kumar, Swapan Kumar Ghorai, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8557720/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 Recent advances in quantum communication demand the development of a robust quantum infrastructure for secure data transmission across multimodal networks. Quantum communication transmits information using quantum states (qubits), which act as fundamental units and are vulnerable to noise, decoherence, and hardware imperfections in optical networks. This paper presents a fault-tolerant framework for quantum communication. It integrates Clifford hierarchy-based diagonal gates with Calderbank-Shor-Steane (CSS) codes to ensure error-resilient operation. The proposed scheme uses recursive algebraic structures, including transversal Clifford gates (T, CZ, CCZ). It also employs concatenated Reed-Muller code families to build logical operators that maintain fault tolerance under realistic channel conditions. The recursive algebraic structure of the Clifford hierarchy and the application of quantum Reed-Muller code families in this study provide reliable fault tolerant links and quantum key distribution (QKD) mechanisms for effective noise mitigation. Channel modeling is performed for both fiber-based and free-space optical links, incorporating depolarizing noise, photon loss, and detector dark counts to evaluate system reliability. The Steane and Reed-Muller codes effectively depolarize noise and minimize the logical error rate to an optimum level. Simulation results demonstrate that the proposed coding scheme reduces logical error rates by nearly an order of magnitude compared to unencoded qubits, maintains state fidelity above 0.9 under moderate loss conditions, and achieves secure key rates well beyond the 7% QBER threshold of the conventional BB84 protocol. The results extend the operational noise tolerance of QKD systems under realistic fiber-based conditions and highlight the framework’s adaptability to free-space optical channels. Overall, the developed framework bridges the gap between mathematical fault-tolerant code design and practical quantum communication architectures. Quantum communication Clifford Hierarchy Calder-bank-Shor-Steane Codes Quantum key distribution Quantum Reed-Muller codes Fault-tolerant quantum networks. 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-8557720","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":595625084,"identity":"76c52f38-acc7-45a3-ac99-b4777fa6d788","order_by":0,"name":"Mahendra Kumar Das","email":"","orcid":"","institution":"Birla Institute of Technology, Mesra, Off Campus Deoghar","correspondingAuthor":false,"prefix":"","firstName":"Mahendra","middleName":"Kumar","lastName":"Das","suffix":""},{"id":595625085,"identity":"d5b69e2d-5eff-4fac-a890-b0bba081e028","order_by":1,"name":"Payal Bhardwaj","email":"","orcid":"","institution":"Birla Institute of Technology, Mesra, Off Campus Deoghar","correspondingAuthor":false,"prefix":"","firstName":"Payal","middleName":"","lastName":"Bhardwaj","suffix":""},{"id":595625086,"identity":"66819095-3818-4e81-b0e6-ada3dd01ecb7","order_by":2,"name":"Bishnu Kumar","email":"","orcid":"","institution":"Birla Institute of Technology, Mesra, Off Campus Deoghar","correspondingAuthor":false,"prefix":"","firstName":"Bishnu","middleName":"","lastName":"Kumar","suffix":""},{"id":595625087,"identity":"abda24ee-f9c9-4598-a985-3d28f96d3fe0","order_by":3,"name":"Swapan Kumar Ghorai","email":"","orcid":"","institution":"Birla Institute of Technology, Mesra, Off Campus Deoghar","correspondingAuthor":false,"prefix":"","firstName":"Swapan","middleName":"Kumar","lastName":"Ghorai","suffix":""},{"id":595625088,"identity":"653b9f13-4836-4769-9e96-0639c4da21de","order_by":4,"name":"Rajesh Kumar Lal","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYDACHuYGhgcVB3iQhBgbCGgBKkg4c4AHSQ8xWhLbDjDw4FeGBMx7DjZ+SJx3R8Ze7PDhzxU1DPL8DcxtD/BpkTnb2CyRuO0ZD490WprkmWMMhjMOMLYb4NMiwc/YANRyGKglx4yxgY2BcQMDY5sEAS3NPxLngLTkf/7Y8I/BnrAW3sY2icQGsC0Mko1tDImEtfAcbLNIOAb0y+00M8nGPonkGYcJakk+fONDzR179tnJjz82fLOx7W9vf4ZXC4YRDAzMpKgfBaNgFIyCUYAVAAB4t0XNftRAagAAAABJRU5ErkJggg==","orcid":"","institution":"Birla Institute of Technology, Mesra, Off Campus Deoghar","correspondingAuthor":true,"prefix":"","firstName":"Rajesh","middleName":"Kumar","lastName":"Lal","suffix":""}],"badges":[],"createdAt":"2026-01-09 07:08:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8557720/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8557720/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104621247,"identity":"5821a745-1b76-4eb5-844e-738c9912ce10","added_by":"auto","created_at":"2026-03-14 09:41:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":757454,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptQIP.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8557720/v1_covered_bef64321-4d1f-41d1-86c6-8d0e622b156e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Fault-Tolerant Quantum Communication Systems Using Clifford Hierarchy-based CSS Codes","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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 communication, Clifford Hierarchy, Calder-bank-Shor-Steane Codes, Quantum key distribution, Quantum Reed-Muller codes, Fault-tolerant quantum networks.","lastPublishedDoi":"10.21203/rs.3.rs-8557720/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8557720/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRecent advances in quantum communication demand the development of a robust quantum infrastructure for secure data transmission across multimodal networks. Quantum communication transmits information using quantum states (qubits), which act as fundamental units and are vulnerable to noise, decoherence, and hardware imperfections in optical networks. This paper presents a fault-tolerant framework for quantum communication. It integrates Clifford hierarchy-based diagonal gates with Calderbank-Shor-Steane (CSS) codes to ensure error-resilient operation. The proposed scheme uses recursive algebraic structures, including transversal Clifford gates (T, CZ, CCZ). It also employs concatenated Reed-Muller code families to build logical operators that maintain fault tolerance under realistic channel conditions. The recursive algebraic structure of the Clifford hierarchy and the application of quantum Reed-Muller code families in this study provide reliable fault tolerant links and quantum key distribution (QKD) mechanisms for effective noise mitigation. 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