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

Abstract

An Aubry-Andr\'{e}-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.