A Block-Encoding Method for Constant and Variable Delay Linear Delay Differential Equations

A Block-Encoding Method for Constant and Variable Delay Linear Delay Differential Equations | 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 A Block-Encoding Method for Constant and Variable Delay Linear Delay Differential Equations Snayhin Sharma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8169166/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 Delay Differential Equations (DDEs) are used to model many systems in medicine, chemistry, and environmental science, and are characterized by the derivative of the function being dependent on the solution in both the present and the past. They are utilized in realistic systems where the transfer between states is not instantaneous, or there is delayed activation of some component. While much literature has been focused on creating quantum algorithms for ODEs, there is no such research considering DDEs. We extend the method of solving lin ear delay functions as a matrix equation to first-order DDEs by creating custom quantum block-encoding oracles for the coefficient matrix resulting from both constant and variable-delays. The findings now allow this new class of equations to be solved faster than linear time with quantum linear system solvers. differential equation modeling linear system quantum algorithm delay differential equations Full Text Additional Declarations No competing interests reported. Supplementary Files ResearchData.xlsx 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-8169166","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":549947367,"identity":"befdfc54-a4e3-49e5-a1c8-9e868300fa6b","order_by":0,"name":"Snayhin 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They are utilized in realistic systems where the transfer between states\n is not instantaneous, or there is delayed activation of some component. While\n much literature has been focused on creating quantum algorithms for ODEs,\n there is no such research considering DDEs. We extend the method of solving lin\near delay functions as a matrix equation to first-order DDEs by creating custom\n quantum block-encoding oracles for the coefficient matrix resulting from both\n constant and variable-delays. 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