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arXiv · 2507.21036

Quantum optical shallow networks

Simone Roncallo·Angela Rosy Morgillo·Seth Lloyd·Chiara Macchiavello·Lorenzo Maccone
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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.

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Simone Roncallo, Angela Rosy Morgillo, Seth Lloyd, Chiara Macchiavello, Lorenzo Maccone. 2025-07-28. Quantum optical shallow networks. https://doi.org/10.1088/2058-9565%2Fae73af

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