Figure 2

Different linear quantum photonic circuit configurations for supervised machine learning. (a) Parameterized circuit comprising three spatial modes for fitting of Fourier series and binary classification. One encoding phase shifter is used per classical data feature. (b, c) Two spatial mode circuits for implementing kernel-based machine learning using Gaussian kernels with photon number-resolving detectors. Here H denotes a 50–50 beamplitter, with matrix elements the same as the Hadamard transform [54, 55]. In other words, (b) is a (c) Mach-Zehnder interferometer. Direct implementation of the kernel method can be done by using the phase shifter to encodes the squared distance between pairs of data points, \(\phi = \delta = ({\mathbf{x}}-{\mathbf{x}}')^{2}\), while random kitchen sink approach approximate a Gaussian kernel using a set of randomized input features \(\phi = x_{r,i} = \gamma ( \boldsymbol{w}_{r}\cdot \boldsymbol{x}_{i}+ b_{r})\)