Figure 4

Binary classification using the three mode linear quantum photonic circuit of Fig. 2(a) with different input Fock states , , and , training using 60 points with a regularization weight \(\alpha = 0.2\). First row: linearly-separable dataset. Middle row: circle dataset. Bottom row: moon dataset. The performance on a test set (red and blue solid cross) of 40 points is given in the upper left corner of each respective subplot. The classification boundaries for all datasets become more complicated as the number of input photons increases, illustrating the increasing expressive power. Increase of expressive power does not affect the trainability of the linear dataset, since a linear classifier suffices. The performance for the circle dataset degrades for larger input photons due to over-fitting, demonstrating that a larger expressive power is not necessarily better. On the other hand, a higher expressive power is necessary in order to accurately classify the moon dataset