Distributed Quantum Neural Networks on Distributed Photonic Quantum Computing

TL;DR

The paper tackles parameter-efficient training of classical neural networks by distributing photonic quantum neural networks (QNNs) across architectures and mapping their high-dimensional measurement statistics to CNN weights via an MPS model. It leverages universal linear-optical decompositions to compress trainable quantum parameters, enabling a target CNN with many more parameters to be generated from a compact quantum footprint, and demonstrates MNIST classification with competitive accuracy at markedly reduced parameter counts. The key contributions include the unitary-decomposition framework, gradient propagation across quantum-classical boundaries, a detailed empirical assessment against classical baselines, and a comprehensive noise analysis showing robustness to near-term photonic hardware imperfections. The results indicate a practical pathway for distributed quantum machine learning that combines the expressivity of photonic Hilbert spaces with the deployability of classical networks, highlighting significant potential for scalable, room-temperature quantum–classical learning pipelines.

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 $χ$. Empirical validation on MNIST classification demonstrates that photonic QT achieves an accuracy of $95.50\% \pm 0.84\%$ using 3,292 parameters ($χ= 10$), compared to $96.89\% \pm 0.31\%$ for classical baselines with 6,690 parameters. Moreover, a ten-fold compression ratio is achieved at $χ= 4$, 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'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.

Figures (7)

• Figure 1: Schematic of quantum-centric supercomputing based on a distributed photonic quantum-computing architecture.
• Figure 2: Overview of the Distributed Photonic Quantum Neural Network (DQNN) framework with unitary decomposition and MPS-based mapping. The system comprises two PQCs, $\text{QNN}_{(1)}$ and $\text{QNN}_{(2)}$, consisting of 9 and 8 optical modes, respectively. Each PQC encodes a trainable unitary $U(\vec{\theta}^{(i)}) \in \mathrm{U}(M_i)$ implemented via a universal decomposition into beam-splitters and phase shifters. Upon injecting $N_i$ photons into $M_i$-mode interferometers, the resulting measurement statistics $P_1 \in [0,1]^{126}$ and $P_2 \in [0,1]^{70}$ span a high-dimensional simplex. These probability vectors are combined via a tensor product $P_w = P_1 \otimes P_2 \in [0,1]^{8820}$ to form the source of weight candidates for a classical convolutional neural network (CNN). The mapping from $[0,1]^{8820}$ to $\mathbb{R}^{8820}$ is performed using a Matrix Product State (MPS) model, $G_b$, which is trained to project $P_w$ into a lower-dimensional subspace containing the target CNN weights $w_{\text{CNN}} \in \mathbb{R}^{6690}$. The CNN is trained to classify inputs using the QNN-generated weights and is evaluated with a cross-entropy loss. Optimization is conducted using the COBYLA algorithm for quantum circuit parameters $\vec{\theta}^{(i)}$, and the ADAM optimizer for classical MPS parameters $b$.
• Figure 3: Schematic of a reconfigurable integrated photonic circuits. The device is structured into three main parts: (1) photon generation and initialization using on-chip photon sources and spectral filters; (2) quantum state evolution through a programmable interferometric network of tunable beam splitters and phase shifters, dynamically controlled by a software-controlled power supply; and (3) Photon detection using superconducting nanowire single-photon detectors (SNSPDs) or photon number resolution detectors (PNRDs).
• Figure 4: Training metrics of the photonic QT framework. (a) Training loss versus epochs for different bond dimensions. (b) Training accuracy versus epochs for different bond dimensions. Higher bond dimensions lead to lower loss and higher accuracy, underscoring the enhanced representational capacity of the photonic QT approach.
• Figure 5: Testing accuracy and generalization error across parameter-efficient training methods. (a) Testing accuracy for photonic QT, classical weight sharing, pruning, and the original CNN. (b) Generalization error of photonic QT compared to the original CNN baseline. Photonic QT achieves competitive accuracy with significantly fewer parameters, albeit with an increased generalization error as model size grows.