Parity-Constrained Quantum Reservoir Computing for Image Classification: Formal Guarantees and Staged Simulation Evidence

Abstract

Quantum reservoir computing has recently reported encouraging image-classification performance, yet many claims remain sensitive to fairness controls, measurement-policy confounds, and benchmark selection. We study a parity-constrained evaluation program for PCA-encoded image inputs and transverse-Ising-style reservoir dynamics, and we combine formal analysis with staged simulation evidence under fixed CPU-only constraints. First, we formulate advantage assessment as a bi-level optimization problem with matched preprocessing, readout family, observable budget, and search budget across quantum and classical branches, and we prove that parity-controlled deltas cannot exceed naive deltas computed with asymmetric policy optimization. Second, we formalize a non-monotone entanglement-utility criterion, showing that boundary derivative sign changes and interior concavity imply a unique interior optimum in coupling strength. Third, we derive an operator-attribution framework based on balanced crossed random effects and prove range and unbiasedness properties for operator-share estimators. Using a staged validation run over MNIST, Fashion-MNIST, EMNIST Balanced, Kuzushiji-MNIST, and a grayscale PCA variant of CIFAR-10, we observe conditional practical advantage on one hard dataset under a pre-registered acceptance tuple, consistent interior-optimum signatures in the tested regime, and strong operator-share estimates with parity-audit closure. These results support a guarded conclusion: formal guarantees are strong, empirical gains are conditional, and attribution quality improves materially when parity is enforced at the row level.