Average Quantum Relative Entropy and Transpilation Depth as Indicators of Noise Robustness in Quantum Binary Classification

Abstract Quantum machine learning models trained under ideal (noiseless) conditions often exhibit significant performance degradation when executed on noisy quantum systems. Ideal simulation accuracy or circuit depth alone does not explain why classifiers with similar structures can show markedly different robustness. A practical question is therefore what factors can explain this difference in accuracy, and whether it can be anticipated and classically verified before costly hardware execution. We propose combining the average quantum relative entropy between classes and backend-specific transpilation depth as a practical pre-hardware indicator of the discrepancy in accuracy between ideal and noisy execution in Quantum Parameterized Binary Classification(QPBC) models. Average quantum relative entropy captures the distinguishability of learned class states, while transpilation depth serves as a practical indicator for cumulative noise exposure following compilation. Building on distinguishability and the contraction of quantum relative entropy under noisy channels, we theoretically derived indicators for both noisy-execution accuracy and simulation-to-device accuracy loss. We support this analysis with controlled experiments across multiple QPBC architectures, ansatz families, encoding methods, measurement strategies, datasets, and noisy backends. Our results show that classifiers with similar ideal accuracy and comparable transpilation depth can nonetheless exhibit substantially different degradation under noise. In contrast, the combined behavior of transpilation depth and average quantum relative entropy provides a more consistent interpretation of these robustness differences than either quantity alone. These findings support a practical pre-hardware assessment approach for screening trained quantum classifiers according to expected noisy-execution robustness.