Algorithmic Advantage on a Gate-Based Photonic Quantum Neural Network

TL;DR

This paper demonstrates that gate-based photonic quantum neural networks can be effectively implemented and trained on current hardware, showing potential algorithmic advantages over classical neural networks in certain tasks.

Contribution

It introduces a photonic quantum neural network framework, evaluates its expressive power, and shows it can outperform classical networks with fewer parameters on specific tasks.

Findings

Photonic QNNs achieved lower cross-entropy loss and higher accuracy than matched-parameter ANNs.

A simple 2-parameter QNN successfully solved the XOR problem, outperforming larger classical networks.

Photonic circuits with high effective dimension classified tasks with up to 100% accuracy on real hardware.

Abstract

We report on a gate-based variational quantum classifier implemented with single photons and probabilistic gates, to emulate the standard quantum circuit model framework. We evaluate the expressive power of two deployable quantum neural networks (QNNs) by computing their effective dimension, a capacity measure grounded in a proven generalization-error bound, and compare them with classical artificial neural networks (ANNs) of equivalent trainable-parameter count. Supervised binary classification tasks are used to benchmark performance across photonic and superconducting QNNs, both of which exhibit superior converged (lower) cross-entropy loss and (higher) prediction accuracy relative to matched-parameter ANNs. For a nonlinearly separable task, our photonic QNN with a single pair of trainable parameters successfully converged (loss 0.04 and accuracy 100%), whereas the equivalent ANN failed to learn the decision boundary, saturating at random-guessing performance. We simulate photonic quantum circuits, training them on the XOR problem and a two-class Iris subset using gradient-free optimization, and assess their robustness to sampling errors under realistic noise processes including photon loss and phase-shifter imperfections. Circuits with comparatively high effective dimension were deployed remotely on a six-qubit photonic quantum processor, achieving classification accuracies of up to 100% in both online and offline learning settings. Notably, even the simplest QNN deployed, with just two trainable parameters, successfully solved tasks that classically require ANNs with at least quadruple the number of parameters, suggesting an emergent algorithmic advantage. Overall, these results demonstrate a clear proof-of-principle that gate-based QNNs can be realized and trained effectively on current photonic hardware, providing proof of algorithmic advantage on a gate-based photonic QNN.