A multi-axis diagnostic framework for Hybrid Quantum-Classical Neural Networks in Empirical setting

Abstract Hybrid quantum-classical neural networks (HQNNs) are a promising paradigm in quantum enhaced machine learning, yet their evaluation remains an open challenge constrained by two key issues: reliance on single metrics (e.g., loss or gradients) and synthetic benchmarks that fail to reflect real-world complexities. This work introduces a multi-metric diagnostic framework, that offers a holistic view of HQNN behavior by analyzing primary axes: quantum trainability (gradient norms), model convergence (loss curves), and quantum utility (via the Quantum Contribution Score, QCS). And secondary axes: expressivity, gradient efficiency and entanglement entropy. Across 16 models over real-world and synthetic data with a classical artificial neural network as baseline. Through this framework empirical phenomena in practical evaluations are developed, including gradient recovery after barren plateaus, data and expressivity dependent QCS trends, relation between gradient behaviour and qubit to layer ratio and model convergence despite barren plateaus.