Programmable photonic quantum walks on lattices with cyclic, toroidal, and cylindrical topology

Programmable photonic quantum walks on lattices with cyclic, toroidal, and cylindrical topology | 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 Programmable photonic quantum walks on lattices with cyclic, toroidal, and cylindrical topology Alessio D'Errico, Nazanin Dehghan, Maria Gorizia Ammendola, Lukas Scarfe, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7116032/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 Photonic implementations of unitary processes on lattice structures, such as quantum walks, have been demonstrated across various architectures. However, few platforms offer the combined advantages of scalability, reconfigurability, and the ability to simulate dynamics on lattices with periodic boundary conditions, such as cyclic or toroidal geometries. Here, we employ a recently developed platform that enables the implementation of arbitrary translationally invariant unitary operations on one- and two-dimensional lattices, and demonstrate a natural mechanism for introducing periodic boundary conditions. Our approach leverages direct access to the reciprocal lattice, where discrete sampling of the unitary evolution effectively enforces the desired topology. We program our platform to realize quantum walks on 1D cyclic lattices and 2D lattices with cylindrical or toroidal topologies. The lattice size can be readily tuned by adjusting the sampling density in reciprocal space. By controlling reciprocal-space occupancy, we investigate the dynamics of localized states and wavepackets, observing refocusing behavior, breathing modes modulated by reciprocal-space discretizations, and wavepacket trajectories that reflect the underlying topology. We further demonstrate a form of dimensional reduction by mapping a 2D quantum walk on a cylinder to a 1D walk with a high-dimensional coin. These results establish a versatile platform for realizing a broad class of optical mode transformations within bounded Hilbert spaces. Physical sciences/Optics and photonics/Optical materials and structures/Liquid crystals Physical sciences/Physics/Quantum physics/Quantum simulation Full Text Additional Declarations There is NO Competing Interest. Supplementary Files 1Dand2DQWonperiodiclattices7.pdf Supplementary Materials 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-7116032","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":526036556,"identity":"eb496cc3-ed5b-46e6-928b-5e1f4df78590","order_by":0,"name":"Alessio 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