Calibrated Hybrid Evaluation of Quantum Reservoir Classification Under Finite-Shot and Simulability Constraints

Abstract

Quantum reservoir computing has shown repeated empirical promise for representation learning, but the evidence base for robust quantum advantage in image classification remains fragmented by confounded entanglement controls, heterogeneous readout optimization practices, and weakly standardized finite-shot reporting. This paper presents a hybrid analysis framework that combines formal derivations and controlled simulation evidence for PCA-encoded image classification with fixed reservoir dynamics and output-layer training. The framework integrates four complementary questions: whether an interior entanglement regime improves geometric and predictive quality under parity controls, whether constrained measurement-operator optimization changes the accuracy-cost-shot frontier, whether advantage signals emerge on a calibrated dataset-difficulty ladder rather than saturated easy tasks, and whether finite-shot classically simulable regimes impose a quantitative boundary on cost-adjusted claims. We formalize these questions through explicit objectives, feasible sets, and theorem-level guarantees, and we evaluate them with deterministic decision gates tied to confidence intervals and assumption audits. The resulting evidence is calibrated rather than binary: the finite-shot simulability boundary is supported in the admissible regime, while broad empirical superiority claims remain inconclusive under strict parity criteria. This outcome is practically relevant beyond quantum machine learning because it illustrates a general methodology for integrating proof-level constraints with reproducible benchmarking when computational claims are sensitive to uncertainty, reporting schema, and regime validity.