Certified Regime Mapping for Quantum Reservoir Computing Under Parity-Constrained Evaluation

Abstract

Quantum reservoir computing is frequently evaluated with point-estimate accuracy gains that confound representation effects, readout parity, and computational cost. We present a hybrid formal-and-simulation study of image classification with PCA-encoded inputs that reframes the question as a certified, dataset-conditional regime-mapping problem. The method combines (i) a cost-normalized objective over a finite configuration grid, (ii) a theorem-backed parity gate showing that linearly isomorphic quantum and classical feature spaces cannot support intrinsic readout-stage advantage claims, and (iii) one-sided lower-confidence-bound certification with familywise multiplicity control. Under a fixed policy (τeff = 0.01, τiso = 0.05, αFWER = 0.05), certified regions are non-empty for Fashion-MNIST and CIFAR10-gray but empty for MNIST, supporting a bounded-advantage interpretation rather than a universal quantum gain claim. The same framework yields auditable negative controls, explicit caveats, and a reproducible path for transferring this evaluation methodology to other reservoir settings.