Fig. 1: Schematic of the components of a quantum photonic neural network.

a Illustrative representation of a neural network represented as a sequence of N layers. Inputs to this network are multi-photon Fock states. Each gray block (U⁽ⁱ⁾) performs a linear-optical transformation, and the red blocks perform the element-wise nonlinear activation function. b Hardware implementation of the linear layer—a multiport interferometer in the CLEMENTS configuration. The insets show the constituent components of the mesh including Mach-Zehnder Interferometers and phase-shifters. c Illustrative representation of the hardware to implement the nonlinear activation function. The atom is a three-level Λ atomic system coupled to an optical cavity as shown in the inset. Transitions of the three-level atom are coupled to a single optical path, i.e., the \(\left\vert {{\rm{g}}}_{{\rm{h}}}\right\rangle \leftrightarrow \left\vert e\right\rangle\) transition is coupled to the red path and the \(\left\vert {{\rm{g}}}_{{\rm{v}}}\right\rangle \leftrightarrow \left\vert e\right\rangle\) transition is coupled to the blue path. The input and output of the nonlinear element are along the modes \({\hat{h}}_{{\rm{in}}}\) and \({\hat{h}}_{{\rm{out}}}\), respectively.