Convolutional Neural Networks (CNNs) are pivotal in computer vision and Big Data analytics but demand significant computational resources when trained on large-scale datasets. Conventional training via back-propagation (BP) with losses like Mean Squared Error or Cross-Entropy often requires extensive iterations and may converge sub-optimally. Quantum computing offers a promising alternative by leveraging superposition, tunneling, and entanglement to search complex optimization landscapes more efficiently. In this work, we propose a hybrid optimization method that combines an Unconstrained Binary Quadratic Programming (UBQP) formulation with Stochastic Gradient Descent (SGD) to accelerate CNN training. Evaluated on the MNIST dataset, our approach achieves a 10--15\% accuracy improvement over a standard BP-CNN baseline while maintaining similar execution times. These results illustrate the potential of hybrid quantum-classical techniques in High-Performance Computing (HPC) environments for Big Data and Deep Learning. Fully realizing these benefits, however, requires a careful alignment of algorithmic structures with underlying quantum mechanisms.

11 pages, 22 figures, accepted in IEEE COMPSAC 2025 Conference. Preprint before peer review