Efficient Quantum Algorithms for Higher-Order Coupled Oscillators

Quantum Physics [Submitted on 22 Apr 2026] Efficient Quantum Algorithms for Higher-Order Coupled Oscillators Caesnan M. G. Leditto, Angus Southwell, Muhammad Usman, Kavan Modi 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 Submission history From: Caesnan Leditto [view email] [v1] Wed, 22 Apr 2026 02:12:43 UTC (6,386 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: math math.DS nlin nlin.AO physics physics.soc-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)