Efficient Quantum Algorithms for Higher-Order Coupled Oscillators
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Quantum Physics arXiv:2604.20108 (quant-ph) [Submitted on 22 Apr 2026] Title:Efficient Quantum Algorithms for Higher-Order Coupled Oscillators Authors:Caesnan M. G. Leditto, Angus Southwell, Muhammad Usman, Kavan Modi View a PDF of the paper titled Efficient Quantum Algorithms for Higher-Order Coupled Oscillators, by Caesnan M. G. Leditto and 3 other authors View PDF HTML (experimental) Abstract:Higher-order networks with multiway interactions can exhibit collective dynamical phenomena that are absent in traditional pairwise network models. However, analyzing such dynamics becomes computationally prohibitive as their state space grows combinatorially in the multiway interaction order. Here we develop quantum algorithms for two central tasks -- synchronization estimation and certification of the no-phase-locking regime -- in the simplicial Kuramoto model. This model is a higher-order generalization of the celebrated Kuramoto model for coupled oscillators on graph-based networks. Under explicit assumptions on data access and types, and simplicial structure, we derive end-to-end quantum gate complexities and identify regimes with polynomial quantum advantage for synchronization estimation and super-polynomial quantum advantage for no-phase-locking certification over classical methods. More broadly, these results extend quantum algorithms for higher-order networks from structural analysis to nonlinear dynamical diagnostics, easing a major computational bottleneck and opening a route to quantum methods for probing higher-order phenomena beyond the reach of direct classical approaches. Subjects: Quantum Physics (quant-ph); Dynamical Systems (math.DS); Adaptation and Self-Organizing Systems (nlin.AO); Physics and Society (physics.soc-ph) Cite as: arXiv:2604.20108 [quant-ph] (or arXiv:2604.20108v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.20108 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Caesnan Leditto [view email] [v1] Wed, 22 Apr 2026 02:12:43 UTC (6,386 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Quantum Algorithms for Higher-Order Coupled Oscillators, by Caesnan M. G. Leditto and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: math math.DS nlin nlin.AO physics physics.soc-ph 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?)