Quantum optical shallow networks

TL;DR

This paper introduces a quantum optical protocol for shallow neural networks that encodes data into single-photon states, leveraging quantum interference effects to achieve scalable and resource-efficient computation.

Contribution

It presents a novel quantum optical implementation of shallow networks that maintains constant resource requirements regardless of network size.

Findings

Uses Hong-Ou-Mandel effect for computation

Achieves constant resource scaling with network size

Demonstrates quantum advantage in neural network implementation

Abstract

Classical shallow networks are universal approximators. Given a sufficient number of neurons, they can reproduce any continuous function to arbitrary precision, with a resource cost that scales linearly in both the input size and the number of trainable parameters. In this work, we present a quantum optical protocol that implements a shallow network with an arbitrary number of neurons. Both the input data and the parameters are encoded into single-photon states. Leveraging the Hong-Ou-Mandel effect, the network output is determined by the coincidence rates measured when the photons interfere at a beam splitter, with multiple neurons prepared as a mixture of single-photon states. Remarkably, once trained, our model requires constant optical resources regardless of the number of input features and neurons.