Distributed Quantum Neural Networks on Distributed Photonic Quantum Computing

Abstract

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 $95.50 \% \pm 0.84 \%$ using 3,292 parameters ($\chi=10$), compared to $96.89 \% \pm 0.31 \%$ for classical baselines with $\mathbf{6, 6 9 0}$ 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 $(10.0 \% \pm 0.5 \%)$. Photonic quantum computing 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.