Hybrid Quantum-Classical Neural Networks for Healthcare Prediction Powered by Automated Scientific Discovery

Hybrid quantum-classical neural networks offer a parameter-efficient path for clinical prediction, yet the field lacks reproducible methodologies for architectural design. Most current models rely on ad hoc circuit choices, complicating replication and comparison. This study introduces a generalizable Hybrid Quantum-Classical Neural Network (HQCNN) framework that replaces trial-and-error design with a principled Bayesian-surprise-guided methodology. Evaluated on the Wisconsin Diagnostic Breast Cancer dataset (n = 569), the framework employs a four-component PCA pipeline feeding a 4-qubit parameterized quantum circuit with two variational layers, integrated within a classical neural pipeline. The model was benchmarked against tuned Support Vector Machine, Random Forest, XGBoost, and Multi-Layer Perceptron baselines under identical 5-fold stratified cross-validation with nested GridSearchCV. The HQCNN achieved 96.49% ± 1.24% accuracy and 99.51% ± 0.38% AUC, outperforming a structurally comparable MLP while using 11.27% fewer trainable parameters (441 versus 497). A circuit-depth ablation identified two variational layers as optimal, consistent with barren-plateau dynamics. KL divergence scores of 0.925, 0.804, and 0.653 nats quantified the epistemic informativeness of competitive accuracy, optimal shallow depth, and parameter efficiency, respectively, while the AI2 AutoDiscovery platform independently validated preprocessing choices post hoc. These results indicate that the primary near-term value of hybrid models in healthcare lies in empirical parameter efficiency rather than raw accuracy gains. Fewer parameters reduce overfitting risk on small medical datasets, lower deployment costs, and produce models that are easier to audit for clinical governance. The Bayesian-surprise methodology finally provides the reproducible, principled design framework that the field has long lacked.