Expressive Power and Limitations of Multi-photon Quantum Neural Networks

Abstract:Quantum neural networks (QNNs) have shown promise in leveraging quantum computation for machine learning tasks. Utilizing multiple identical photons as input, multi-photon quantum neural networks (MPQNNs) have the potential to enhance the expressivity through increasing the photon number. However, how precisely the expressivity of an MPQNN is affected by an increase in photon number, and whether it can be infinitely enhanced by increasing the photon number, remains unexplored. In this work, we quantitatively estimate the expressivity of this model by deriving upper bounds on approximation error in two cases. In the case of a fixed observable, there exists a threshold that scales linearly with the mode number. Below the threshold, the expressivity of an MPQNN can be enhanced polynomially by increasing the photon number. Above the threshold, however, increasing the photon number does not affect the expressivity. In the case of a trainable observable, the expressivity can always be enhanced polynomially by increasing the photon number. These findings are then validated by numerical simulations. Our work elucidates the performance enhancement of multi-photon quantum feature in QNNs, as well as its limitations, offering guidance for leveraging multi-photon advantages in quantum machine learning.

arXiv:2608.01365 [quant-ph]

(or arXiv:2608.01365v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.01365 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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