Structured Quantum Kernels for Chaotic Forecasting

Quantum Physics arXiv:2609.13360 (quant-ph) [Submitted on 11 Sep 2026] Title:Structured Quantum Kernels for Chaotic Forecasting Authors:Zhihui Wang, Sujit Roy, Ata Akbari, Manil Maskey, Rahul Ramachandran View a PDF of the paper titled Structured Quantum Kernels for Chaotic Forecasting, by Zhihui Wang and 4 other authors View PDF HTML (experimental) Abstract:Quantum kernels promise exponentially large feature spaces, but expressive circuits render their Gram matrices uninformative, bandwidth tuning collapses them toward classical RBF, and the practical consensus is that quantum kernels add nothing on classical data. We answer another productive question, an architectural one: whether the structure of an encoding circuit can carry an inductive bias that tuned classical kernels lack. We introduce AeRot, a quantum kernel fusing amplitude encoding of l2-normalized delay windows with a grouped single-qubit rotation layer that assigns contiguous temporal blocks to each qubit, making the circuit delay-window-aware. On Lorenz-63 kernel ridge regression with cross-validated bandwidths over 100 seeds, AeRot outperforms tuned RBF and Matern-5/2, the advantage emerging at physical horizons >= 0.15 tu and reaching +0.137 mean R^2 at 0.25 tu (5 qubits, window 32). Linear-stability analysis of the window tail localises the advantage to the unstable saddle-approach regime: AeRot wins 83% of windows in the most unstable decile, with the win rate rising monotonically with tail instability and a sign flip at the local stability boundary. The difficulty is fold-branch ambiguity: trajectories approaching the saddle are locally diverging, and Euclidean kernels struggle to resolve which lobe the trajectory will commit to. Structural diagnostics confirm Gram matrices structurally distinct from tuned RBF, with strictly higher target-kernel alignment at every horizon. The gain is architectural: a finite-sample inductive-bias effect of temporally structured encoding on a folded attractor, with no computational-separation claim attached. To our knowledge this is the first mechanistic localisation of quantum-kernel advantage to a specific dynamical regime of a classical system. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.13360 [quant-ph] (or arXiv:2609.13360v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.13360 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zhihui Wang [view email] [v1] Fri, 11 Sep 2026 17:50:40 UTC (1,112 KB) Full-text links: Access Paper: View a PDF of the paper titled Structured Quantum Kernels for Chaotic Forecasting, by Zhihui Wang and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)