Practical Quantum-Classical Feature Fusion for complex data Classification

Hybrid quantum and classical learning aims to couple quantum feature maps with the robustness of classical neural networks, yet most architectures treat the quantum circuit as an isolated feature extractor and merge its measurements with classical representations by direct concatenation. This neglects that the quantum and classical branches constitute distinct computational modalities and limits reliable performance on complex, high dimensional tabular and semi structured data, including remote sensing, environmental monitoring, and medical diagnostics. We present a multimodal formulation of hybrid learning and propose a cross attention mid fusion architecture in which a classical representation queries quantum derived feature tokens through an attention block with residual connectivity. The quantum branch is kept within practical NISQ budgets and uses up to nine qubits. We evaluate on Wine, Breast Cancer, Forest CoverType, FashionMNIST, and SteelPlatesFaults, comparing a quantum only model, a classical baseline, residual hybrid models, and the proposed mid fusion model under a consistent protocol. Pure quantum and standard hybrid designs underperform due to measurement induced information loss, while cross attention mid fusion is consistently competitive and improves performance on the more complex datasets in most cases. These findings suggest that quantum derived information becomes most valuable when integrated through principled multimodal fusion rather than used in isolation or loosely appended to classical features.

A Geometric-Aware Perspective and Beyond: Hybrid Quantum-Classical Machine Learning Methods

Geometric Machine Learning (GML) has shown that respecting non-Euclidean geometry in data spaces can significantly improve performance over naive Euclidean assumptions. In parallel, Quantum Machine Learning (QML) has emerged as a promising paradigm that leverages superposition, entanglement, and interference within quantum state manifolds for learning tasks. This paper offers a unifying perspective by casting QML as a specialized yet more expressive branch of GML. We argue that quantum states, whether pure or mixed, reside on curved manifolds (e.g., projective Hilbert spaces or density-operator manifolds), mirroring how covariance matrices inhabit the manifold of symmetric positive definite (SPD) matrices or how image sets occupy Grassmann manifolds. However, QML also benefits from purely quantum properties, such as entanglement-induced curvature, that can yield richer kernel structures and more nuanced data embeddings. We illustrate these ideas with published and newly discussed results, including hybrid classical -quantum pipelines for diabetic foot ulcer classification and structural health monitoring. Despite near-term hardware limitations that constrain purely quantum solutions, hybrid architectures already demonstrate tangible benefits by combining classical manifold-based feature extraction with quantum embeddings. We present a detailed mathematical treatment of the geometrical underpinnings of quantum states, emphasizing parallels to classical Riemannian geometry and manifold-based optimization. Finally, we outline open research challenges and future directions, including Quantum Large Language Models (LLMs), quantum reinforcement learning, and emerging hardware approaches, demonstrating how synergizing GML and QML principles can unlock the next generation of machine intelligence.