Figure 1

Circuit diagram of parameterized linear quantum photonic circuit with m-spatial modes and encoding data x using a single phase shifter. The expectation value with respect to observables of photon-number resolving (PNR) or threshold detectors can be written as a Fourier series \(\sum_{\omega} c_{\omega}e^{i\omega x}\), with frequencies ω determined by the number of photons fed into the circuit, while the coefficients \(c_{\omega}\) are determined by the trainable circuit blocks and the observable