Multiple photons enhance quantum machine learning

Photons are promising candidates for quantum information technology due to their high robustness and long coherence time at room temperature. Inspired by recent advances in photonic computing techniques, research has increasingly turned to quantum machine learning (QML) on photonic platforms. Although photons provide a high-dimensional quantum feature space suitable for computation, a general understanding of how photon number can be harnessed for learning tasks remains limited. Here, we establish both theoretically and experimentally a learning-capacity advantage of multi-photon states over single-photon states in photonic QML. We prove that the learning capacity of linear optical circuits, quantified by the rank of the data quantum Fisher information matrix, scales polynomially with the photon number. This scaling enables multi-photon models to generalize from fewer training states than corresponding single-photon models and to achieve lower test loss under the same architecture and learning protocol. Moreover, we experimentally corroborate these findings through unitary learning and metric learning tasks, by performing online training on a fully programmable photonic integrated platform. Our work highlights the potential of photonic QML and paves the way for achieving quantum enhancement in practical machine learning applications.