When do quantum views help? Complementary classical-quantum representations in multi-view fusion

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.

Large machine learning models benefit substantially from multimodal inputs that provide a complementary view of the same example. We introduce QUIVER (QUantum-Informed Views for Enhanced Representations, a paradigm that enriches classical data-driven features with a quantum Fisher view: a geometrically motivated, basis-independent summary of higher-order correlations captured by a variational quantum circuit (VQC) trained to perform the same task. Unlike classical feature augmentation, the quantum Fisher information matrix encodes the intrinsic geometry of the learned quantum state manifold. While this feature map, motivated by quantum information theory, is ordinarily non-trivial to model classically, it can surface statistical structure that additional classical data or model capacity finds difficult to learn. This makes the quantum Fisher view a genuinely complementary modality rather than a redundant one. We demonstrate that QUIVER improves standard performance metrics on two benchmark datasets from very different fields: QM9 for predicting molecule properties, and JetClass for predicting jet flavor at the Large Hadron Collider (LHC). The core contribution, however, is domain-agnostic: the quantum Fisher view can be fused into a broad class of model architectures via targeted modifications to the base architecture, to incorporate information about the quantum geometry of the problem. These results demonstrate that quantum-geometric features, extracted from simulated variational circuits, can deliver measurable value for standard machine learning tasks, well before the advent of fault-tolerant quantum hardware.

Variational quantum circuits (VQCs) are highly sensitive to circuit architecture, yet most quantum machine learning pipelines select a single best design and discard the remaining candidates. This paper addresses whether the structural diversity across quantum circuit search spaces can be used to produce stronger predictions through model fusion. We apply Combinatorial Fusion Analysis (CFA), a model fusion framework that selects and combines multiple scoring systems using rank-score function (RSF) and cognitive diversity (CD), to a pool of 29 architecturally diverse classical models and quantum circuits. Using a diversity-aware model selection method, we identify subsets of maximally diverse models and combine them with both score and rank combination. Experiments on four binary classification benchmarks covering different domains demonstrate that CFA-based hybrid classical-quantum fusion consistently outperform the best individual model on every dataset considered with improvements up to 6.03% in accuracy. When comparing with relevant literatures, the CFA framework further achieves superior performance across all four datasets.