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.
@article{arxiv.2507.21036,
title = {Quantum optical shallow networks},
author = {Simone Roncallo and Angela Rosy Morgillo and Seth Lloyd and Chiara Macchiavello and Lorenzo Maccone},
journal= {arXiv preprint arXiv:2507.21036},
year = {2025}
}