One-Dimensional Nonlinear Quantum Walks
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Quantum Physics arXiv:2605.20464 (quant-ph) [Submitted on 19 May 2026] Title:One-Dimensional Nonlinear Quantum Walks Authors:Yujia Shi, Thomas G. Wong View a PDF of the paper titled One-Dimensional Nonlinear Quantum Walks, by Yujia Shi and 1 other authors View PDF HTML (experimental) Abstract:We explore a continuous-time quantum walk starting at a single vertex on the discrete path and cycle with a cubic nonlinearity. Such nonlinearities arise in Bose-Einstein condensates described by the Gross-Pitaevskii equation or by nonlinear optical waveguide arrays. We analytically prove that the nonlinear quantum walk can be trapped to arbitrary fidelity depending on the coefficient of the nonlinear term. This contrasts with linear quantum walks, which are known for spreading quickly in one dimension. We propose that this trapping can be used for timing in quantum state transfer, where a qubit is held at a node until it is ready to be transferred, and it can also be held again at the receiving node. This scheme can also be interpreted as a form of quantum memory, with the trap and transfer corresponding to the storage and release of quantum information. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.20464 [quant-ph] (or arXiv:2605.20464v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.20464 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Yujia Shi [view email] [v1] Tue, 19 May 2026 20:24:51 UTC (151 KB) Full-text links: Access Paper: View a PDF of the paper titled One-Dimensional Nonlinear Quantum Walks, by Yujia Shi and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)