High-Fidelity Quantum Simulation of Braiding Statistics and Non-Abelian Holonomic Gates Using Stückelberg Interferometry with Demkov–Kunike Pulses

High-Fidelity Quantum Simulation of Braiding Statistics and Non-Abelian Holonomic Gates Using Stückelberg Interferometry with Demkov–Kunike Pulses | 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 High-Fidelity Quantum Simulation of Braiding Statistics and Non-Abelian Holonomic Gates Using Stückelberg Interferometry with Demkov–Kunike Pulses Fai Fanyuy Nyuydze, Lukong Cornelius Fai, Afungchui David, Tabod Charles Tabod This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8818108/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 Geometric phases and holonomies offer a robust route to quantum control and simulation. We introduce a high-fidelity quantum simulation framework based on the analytically solvable Demkov-Kunike (DK) model, which extends the standard Landau-Zener paradigm by providing richer control over evolution paths. We demonstrate how tailored DK pulse sequences can simulate the braiding statistics of Abelian anyons through Stückelberg interferometry, with a protocol for exact dynamical phase cancellation. Generalizing to a three-level Λ-system, we engineer a non-Abelian Wilczek-Zee connection and construct a universal set of holonomic quantum gates. A detailed analysis of the evolution operator and leakage probability for the three-level DK model is provided, identifying optimal adiabaticity regimes for high fidelity. We propose an experimental implementation using trapped ions, including a rigorous derivation of the effective DK Hamiltonian in a decoherence-free subspace. Numerical simulations confirm the expected interference signatures, gate non-commutativity, and enhanced robustness of geometric gates under decoherence. This work establishes DK pulses as a versatile tool for simulating topological-like phenomena and engineering geometric quantum gates in controllable quantum systems. Theoretical Physics Geometric phases Holonomic quantum gates Demkov-Kunike model Stückelberg interferometry Quantum simulation Trapped ions Full Text Additional Declarations The authors declare no competing interests. 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. 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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-8818108","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":587640583,"identity":"45c6d97f-859e-4a76-a6eb-e60f9d346370","order_by":0,"name":"Fai Fanyuy Nyuydze","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3UlEQVRIiWNgGAWjYBAC9gbGhg9QFpAwsCCshecAY+MMKAukRYIYLQyMEC0SCWCSCC3shxsbfu44nLjh5vOrG34USDDwt3cn4NfCk9jY2HsGqOV2TtnNHqDDJM6c3YBXiz1DYvsD3jawlrQbPEAtBhK5+LXw8D9sbPwL0nLzTNrNP0RpkUhsbAbbcoP92G3ibJF42Ngs25ZuPPNMDtttGQMJHoJ+4eFPf9j4ts1atu/48Wc33/yxkeNv78WvBQqaGRQO8BiAzSBGOQjUMcg3sD8gVvUoGAWjYBSMMAAAc9dRujnj47cAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0008-3947-8657","institution":"University of Bamenda","correspondingAuthor":true,"prefix":"","firstName":"Fai","middleName":"Fanyuy","lastName":"Nyuydze","suffix":""},{"id":587640584,"identity":"8dad5ad0-e6ae-477a-bc15-363f935340c9","order_by":1,"name":"Lukong Cornelius Fai","email":"","orcid":"https://orcid.org/0000-0002-5079-2080","institution":"University of Buea","correspondingAuthor":false,"prefix":"","firstName":"Lukong","middleName":"Cornelius","lastName":"Fai","suffix":""},{"id":587640585,"identity":"4ce566e1-b694-4bdb-98a0-73e03a2af081","order_by":2,"name":"Afungchui David","email":"","orcid":"","institution":"University of Bamenda","correspondingAuthor":false,"prefix":"","firstName":"Afungchui","middleName":"","lastName":"David","suffix":""},{"id":587640586,"identity":"da4c09b9-644c-4040-ad0d-0b320b4505f9","order_by":3,"name":"Tabod Charles Tabod","email":"","orcid":"","institution":"University of Bamenda","correspondingAuthor":false,"prefix":"","firstName":"Tabod","middleName":"Charles","lastName":"Tabod","suffix":""}],"badges":[],"createdAt":"2026-02-07 21:50:08","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8818108/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8818108/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102297899,"identity":"d8140159-bb59-4f9c-8911-f1fdf228c243","added_by":"auto","created_at":"2026-02-10 10:29:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":562213,"visible":true,"origin":"","legend":"","description":"","filename":"FaiFanyuyNyuydzepaperI01February2026.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8818108/v1_covered_93fd3a56-acc2-41ee-bc87-92c6614c1138.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eHigh-Fidelity Quantum Simulation of Braiding Statistics and Non-Abelian Holonomic Gates Using Stückelberg Interferometry with Demkov–Kunike Pulses\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Bamenda","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":"Geometric phases, Holonomic quantum gates, Demkov-Kunike model, Stückelberg interferometry, Quantum simulation, Trapped ions","lastPublishedDoi":"10.21203/rs.3.rs-8818108/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8818108/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGeometric phases and holonomies offer a robust route to quantum control and simulation. We introduce a high-fidelity quantum simulation framework based on the analytically solvable Demkov-Kunike (DK) model, which extends the standard Landau-Zener paradigm by providing richer control over evolution paths. We demonstrate how tailored DK pulse sequences can simulate the braiding statistics of Abelian anyons through St\u0026uuml;ckelberg interferometry, with a protocol for exact dynamical phase cancellation. Generalizing to a three-level Λ-system, we engineer a non-Abelian Wilczek-Zee connection and construct a universal set of holonomic quantum gates. A detailed analysis of the evolution operator and leakage probability for the three-level DK model is provided, identifying optimal adiabaticity regimes for high fidelity. We propose an experimental implementation using trapped ions, including a rigorous derivation of the effective DK Hamiltonian in a decoherence-free subspace. Numerical simulations confirm the expected interference signatures, gate non-commutativity, and enhanced robustness of geometric gates under decoherence. 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