Quantum Stochastic Walks for Portfolio Optimization: Theory and Implementation on Financial Networks

Quantum Stochastic Walks for Portfolio Optimization: Theory and Implementation on Financial Networks | 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 Quantum Stochastic Walks for Portfolio Optimization: Theory and Implementation on Financial Networks Yen Jui Chang, Wei-Ting Wang, Yun-Yuan Wang, Chen-Yu Liu, Kuan-Cheng Chen, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7045880/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Financial markets are noisy yet contain a latent graph–theoretic structure that can be exploited for superior risk-adjusted returns. We propose a \emph{quantum-stochastic-walk} (QSW) optimizer that embeds assets in a weighted graph—nodes are securities, edges encode the return–covariance kernel—and derives portfolio weights from the stationary distribution of the walk. Three empirical studies support the method. (i)~On the \textbf{Top-100 S\&P constituents} (2016–2024) six scenario portfolios fitted on 1- and 2-year windows lift the out-of-sample Sharpe ratio by up to \textbf{+27\,\%} while slashing annual turnover from $480\%$ (mean–variance) to $2$–$90\%$. (ii)~A \mbox{$625$} grid search isolates a robust sweet-spot—$\alpha,\lambda\!\lesssim\!0.5$, $\omega\!\in[0.2,0.4]$—that delivers Sharpe $\approx0.97$ at $\le5\%$ turnover and Herfindahl–Hirschman index(HHI) ${\sim}0.01$. (iii)~Repeating the full grid on \textbf{50 random 100-stock subsets} of the S\&P\,500 generates 31,350 additional back-tests: the best-per-draw QSW beats re-optimized mean–variance on Sharpe in 54\,\% of samples and \emph{always} wins on trading efficiency, with median turnover \textbf{36\,\%} versus \textbf{351\,\%}. Overall, QSW raises the annualized Sharpe ratio by \textbf{15\,\%} and cuts average turnover by \textbf{90\,\%} relative to classical optimization, all while remaining comfortably within UCITS 5/10/40 rule. The findings demonstrate that hybrid quantum–classical dynamics can uncover non-linear dependencies overlooked by quadratic models, offering a practical low-cost weighting engine for themed ETFs and other systematic mandates. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics quantum finance portfolio optimization quantum stochastic walks complex networks Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 09 Sep, 2025 Reviews received at journal 02 Sep, 2025 Reviews received at journal 22 Aug, 2025 Reviewers agreed at journal 18 Aug, 2025 Reviewers agreed at journal 05 Aug, 2025 Reviewers invited by journal 16 Jul, 2025 Editor assigned by journal 14 Jul, 2025 Submission checks completed at journal 14 Jul, 2025 First submitted to journal 04 Jul, 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-7045880","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":486551915,"identity":"b99bd08f-6e1d-4a73-9722-a27ca1522331","order_by":0,"name":"Yen Jui 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We propose a \\emph{quantum-stochastic-walk} (QSW) optimizer that embeds assets in a weighted graph—nodes are securities, edges encode the return–covariance kernel—and derives portfolio weights from the stationary distribution of the walk. Three empirical studies support the method. (i)~On the \\textbf{Top-100 S\\\u0026amp;P constituents} (2016–2024) six scenario portfolios fitted on 1- and 2-year windows lift the out-of-sample Sharpe ratio by up to \\textbf{+27\\,\\%} while slashing annual turnover from $480\\%$ (mean–variance) to $2$–$90\\%$. (ii)~A \\mbox{$625$} grid search isolates a robust sweet-spot—$\\alpha,\\lambda\\!\\lesssim\\!0.5$, $\\omega\\!\\in[0.2,0.4]$—that delivers Sharpe $\\approx0.97$ at $\\le5\\%$ turnover and Herfindahl–Hirschman index(HHI) ${\\sim}0.01$. (iii)~Repeating the full grid on \\textbf{50 random 100-stock subsets} of the S\\\u0026amp;P\\,500 generates 31,350 additional back-tests: the best-per-draw QSW beats re-optimized mean–variance on Sharpe in 54\\,\\% of samples and \\emph{always} wins on trading efficiency, with median turnover \\textbf{36\\,\\%} versus \\textbf{351\\,\\%}. Overall, QSW raises the annualized Sharpe ratio by \\textbf{15\\,\\%} and cuts average turnover by \\textbf{90\\,\\%} relative to classical optimization, all while remaining comfortably within UCITS 5/10/40 rule. The findings demonstrate that hybrid quantum–classical dynamics can uncover non-linear dependencies overlooked by quadratic models, offering a practical low-cost weighting engine for themed ETFs and other systematic mandates.\u003c/p\u003e","manuscriptTitle":"Quantum Stochastic Walks for Portfolio Optimization: Theory and Implementation on Financial Networks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-21 09:33:36","doi":"10.21203/rs.3.rs-7045880/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-09-09T23:13:53+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-02T21:10:06+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-23T00:41:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"267795237462159425781044709740231236541","date":"2025-08-19T00:59:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"152661603461556747748217560492934820874","date":"2025-08-05T13:07:52+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-07-16T22:14:40+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-07-15T00:09:11+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-07-14T06:48:47+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Unconventional Computing","date":"2025-07-04T10:25:12+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-unconventional-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [npj Unconventional Computing](https://www.nature.com/npjunconvcomput)","snPcode":"44335","submissionUrl":"https://submission.springernature.com/new-submission/44335/3","title":"npj Unconventional Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bbc0c913-43a2-4e2a-bb6e-1ff566b33db3","owner":[],"postedDate":"July 21st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":51654905,"name":"Physical sciences/Engineering"},{"id":51654906,"name":"Physical sciences/Mathematics and computing"},{"id":51654907,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2025-12-24T21:23:26+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-21 09:33:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7045880","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7045880","identity":"rs-7045880","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}