On the Complementarity of Quantum and Classical Features: Adaptive Hybrid Quantum-Classical Feature Fusion for Breast Cancer Classification

The integration of quantum machine learning with classical deep learning offers promising avenues for medical image analysis by mapping data into high-dimensional Hilbert spaces. However, unifying these paradigms remains challenging due to optimization asymmetries. We propose a hybrid quantum-classical architecture for breast cancer diagnosis based on a dual-branch feature-extraction pipeline. Our framework unifies complementary representations from classical models and trainable or deterministic (non-trainable) quantum circuits. Three fusion strategies are introduced: Static Hybrid Fusion (SHF) for offline extraction, Dynamic Hybrid Fusion (DHF) for end-to-end co-adaptation, and Temperature-Scaled Hybrid Fusion (TSHF). Inspired by multimodal learning, TSHF uses a learnable scalar to balance branch gradient dynamics and address optimization bottlenecks. We evaluate BreastMNIST, INbreast, and BUS-UCLM, spanning ultrasound and mammography, using ResNet-18 and a shallow CNN, with five independent runs per configuration. Fusion improves over the strongest classical baseline on all three benchmarks. On BreastMNIST, TSHF with ResNet-18 and a non-trainable circuit achieves 88.33% accuracy, 92.09% F1-score, and 92.09% AUC-ROC, versus 84.74% accuracy and 87.08% AUC-ROC for ResNet-18 alone. On INbreast, SHF with the same pairing performs best, at 70.42% accuracy, 72.96% F1-score, and 80.28% AUC-ROC. On BUS-UCLM, SHF with a trainable circuit achieves 78.46% accuracy and 84.66% F1-score, over seven accuracy points above the best standalone branch. Adaptive fusion is not universally beneficial: static fusion performs best on the two smaller datasets, suggesting an additional estimation burden from co-adaptation and learned calibration under limited data. Clinical applicability requires validation beyond the small, low-resolution datasets and simulated quantum circuits considered here.