Distributed Quantum Neural Networks on Distributed Photonic Quantum Computing

We introduce a distributed quantum-classical framework that synergizes photonic quantum neural networks (QNNs) with matrix-product-state (MPS) mapping to achieve parameter-efficient training of classical neural networks. By leveraging universal linear-optical decompositions of M-mode interferometers and photon-counting measurement statistics, our architecture generates neural parameters through a hybrid quantum-classical workflow: photonic QNNs with M(M+1)/2 trainable parameters produce high-dimensional probability distributions that are mapped to classical network weights via an MPS model with bond dimension chi. Empirical validation on MNIST classification demonstrates that photonic QT achieves an accuracy of 95.50% ± 0.84% using 3,292 parameters (chi = 10), compared to 96.89% ± 0.31% for classical baselines with 6,690 parameters. Moreover, a ten-fold compression ratio is achieved at chi = 4, with a relative accuracy loss of less than 3%. The framework outperforms classical compression techniques (weight sharing/pruning) by 6--12% absolute accuracy while eliminating quantum hardware requirements during inference through classical deployment of compressed parameters. Simulations incorporating realistic photonic noise demonstrate the framework's robustness to near-term hardware imperfections. Ablation studies confirm quantum necessity: replacing photonic QNNs with random inputs collapses accuracy to chance level (10.0% ± 0.5%). Photonic quantum computing's room-temperature operation, inherent scalability through spatial-mode multiplexing, and HPC-integrated architecture establish a practical pathway for distributed quantum machine learning, combining the expressivity of photonic Hilbert spaces with the deployability of classical neural networks.