Hybrid Quantum-Classical Convolutional Neural Networks for Medical Image Classification: A Statistical Validation Framework

We present a hybrid quantum-classical convolutional neural network (QCNN) architecture that integrates variational quantum circuits into classical deep learning frameworks for medical image classification. Our approach uses 4-qubit variational quantum circuits as intermediate processing layers within a traditional CNN, implementing two distinct quantum encoding strategies: amplitude encoding for high dimensional feature compression and angle encoding for direct feature mapping. The hybrid architecture processes the relatively small BreastMNIST medical images through classical feature extraction (yielding 2048 features), quantum preprocessing via dual pathways, and variational quantum circuits with parameterized RY, RZ, and RX rotations connected by CNOT entangling gates. The quantum architecture successfully maintains end to end differentiable training via PennyLane's PyTorch interface.

Two quantum circuits employ different entanglement topologies, linear chain and circular connectivity, generating 10 quantum measurements, which undergo classical fusion with original features for final classification. Statistical validation across 10 independent experimental runs demonstrates quantum model's statistically superior performance with a mean final accuracy of 81.3% versus parameter-matched classical architecture's accuracy of 77.2%. Wilcoxon signed-rank testing confirms statistical significance with p=0.033 and Cohen's d=0.676.

This work addresses statistical validation gaps in quantum machine learning for medical image classification by providing a parameter-matched comparison based on repeated trials that demonstrates a measurable quantum advantage on a small medical dataset. The quantum implementation shows statistically verified consistency advantages, identifying architectural requirements and providing a foundation for quantum- enhanced feature processing as quantum hardware advances.