Quantum Reservoir Computing Under Comparator Parity: Regime-Conditioned Advantage, Entanglement Effects, and Kernel-Null Boundaries

Abstract

Quantum reservoir computing (QRC) is often evaluated with heterogeneous comparator strength, making it difficult to determine whether reported gains are genuinely quantum-mechanistic or induced by feature-map geometry and protocol asymmetry. This paper studies image classification with PCA-compressed inputs, angle encoding, a transverse-Ising reservoir, and partial Pauli-observable readout under strict comparator parity. We combine formal analysis and executed simulation evidence to answer three coupled questions: where advantage regions exist across rank, whether entanglement-observable interactions are consistently positive, and when non-entangling regimes are effectively emulable by classical kernels. The formal component proves a unique ridge readout optimum under parity constraints, identifies the interaction term isolated by a difference-in-differences design, and derives a non-entangling predictor-gap bound linked to kernel-emulation error. The executed simulation component reports contiguous positive confidence intervals against strong classical comparators over multiple rank regimes, mixed interaction effects for entanglement strength, and bound-ratio behavior below unity in tested non-entangling regimes. Together, these findings support a conservative claim boundary: QRC gains are regime-conditioned and auditable under parity controls, broad monotonic entanglement-utility claims are not supported by current evidence, and kernel-null conclusions are restricted to fixed-regularization assumptions under the present proxy-dataset execution setting.