Coined Quantum Walks on Complex Networks for Quantum Computers

Coined Quantum Walks on Complex Networks for Quantum Computers | 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PDF Research Article Coined Quantum Walks on Complex Networks for Quantum Computers Rei Sato This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8661884/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract We propose a quantum circuit design for implementing coined quantum walks on complex networks. In complex networks, the coin and shift operators depend on the varying degrees of the nodes, which makes circuit construction more challenging than for regular graphs. To address this issue, we use a dual-register encoding. This approach enables a simplified shift operator and reduces the resource overhead compared to previous methods. We implement the circuit using Qmod, a high-level quantum programming language, and evaluated the performance through numerical simulations on Erd\H{o}s–R'enyi, Watts–Strogatz, and Barab'asi–Albert models. The results show that the circuit depth scales as approximately $N^{1.9}$ regardless of the network topology. Furthermore, we execute the proposed circuits on the \texttt{ibm_torino} superconducting quantum processor for Watts–Strogatz models with $N=4$ and $N=8$. The experiments show that hardware-aware optimization slightly improved the $L_1$ distance for the larger graph, whereas connectivity constraints imposed overhead for the smaller one. These results indicate that while current NISQ devices are limited to small-scale validations, the polynomial scaling of our framework makes it suitable for larger-scale implementations in the early fault-tolerant quantum computing era. Full Text Additional Declarations No competing interests reported. Supplementary Files supplemental.zip Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 02 Apr, 2026 Reviews received at journal 01 Apr, 2026 Reviewers agreed at journal 07 Mar, 2026 Reviewers invited by journal 02 Mar, 2026 Editor assigned by journal 24 Jan, 2026 Submission checks completed at journal 24 Jan, 2026 First submitted to journal 21 Jan, 2026 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-8661884","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":599307395,"identity":"6f2a999e-2c27-4ec0-87a3-eebaf3c41a7c","order_by":0,"name":"Rei Sato","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArElEQVRIiWNgGAWjYFACxsYHDAVAmhmIE4jU0mzAYECaFgY2CbAWooF5e3NbxQ8DO3v5duYNDA8qiNAic+Zg280eg+TEDYfZChgSzhChRUIise02gwFzggEzjwFDYhsxWuQfthUzGNTbyzcTrUWCsY2ZweAwY8NhorXwJDZL9hgcB/vlAHF+YT/+8MOPimp7+f7DGx/+ICbEkIHBARI1MJAWoaNgFIyCUTCCAAB34y/+3mM4cAAAAABJRU5ErkJggg==","orcid":"","institution":"Classiq Technologies G.K.","correspondingAuthor":true,"prefix":"","firstName":"Rei","middleName":"","lastName":"Sato","suffix":""}],"badges":[],"createdAt":"2026-01-21 16:09:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8661884/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8661884/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104402073,"identity":"de56a67b-3865-4649-ad72-183f4a1ccb62","added_by":"auto","created_at":"2026-03-11 12:14:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":629199,"visible":true,"origin":"","legend":"","description":"","filename":"main.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8661884/v1_covered_109962b6-1645-4019-88aa-fe0bbddfd610.pdf"},{"id":103955835,"identity":"816d5cf0-5fd6-4e8e-b8f2-cc2bcd95c1c0","added_by":"auto","created_at":"2026-03-05 03:07:19","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":147176,"visible":true,"origin":"","legend":"","description":"","filename":"supplemental.zip","url":"https://assets-eu.researchsquare.com/files/rs-8661884/v1/f0091c31787f44b5a2b0a59b.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eCoined Quantum Walks on Complex Networks for Quantum Computers\u003c/p\u003e","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":"quantum-information-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qinp","sideBox":"Learn more about [Quantum Information Processing](http://link.springer.com/journal/11128)","snPcode":"11128","submissionUrl":"https://submission.nature.com/new-submission/11128/3","title":"Quantum Information Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8661884/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8661884/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We propose a quantum circuit design for implementing coined quantum walks on complex networks. 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The experiments show that hardware-aware optimization slightly improved the $L_1$ distance for the larger graph, whereas connectivity constraints imposed overhead for the smaller one. 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