Free-fermion spectral structure enables strange nonchaotic attractor classification in Aubry-Andre-Harper quantum reservoirs

Abstract:An Aubry-André-Harper (AAH) quantum reservoir classifies strange nonchaotic attractors (SNAs) against chaos, substantially outperforming reservoirs built from dense random matrices on the full Fock space. Ablations and controlled interventions identify \emph{free-fermion one-body transition sparsity}, rather than proximity to a quantum phase transition, as the dominant factor under our controls, since $H_0$ is quadratic in fermion operators and only $N(N-1)2^{N-2}=3584$ of the $65{,}280$ Fock-space transitions carry weight. Random on-site disorder, which preserves this quadratic structure, matches AAH accuracy, whereas full-Hilbert-space random matrices and eigenvector permutations, which break it, collapse to the random baseline. We characterize the resulting frequency-selective filtering with a Hamiltonian transition kernel, validate it to $N=8$ qubits, and reproduce it in a second dynamical system. We also use the reservoir as a training-free screen for strange-nonchaotic structure in Kepler RR Lyrae light curves.

arXiv:2609.26825 [quant-ph]

(or arXiv:2609.26825v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.26825 Focus to learn more arXiv-issued DOI via DataCite

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