Fig. 3: Experimental reconstruction of the [3 × 32] sub-matrices and comparison with the Haar-random matrices.
From: Reconfigurable continuously-coupled 3D photonic circuit for Boson Sampling experiments
a Experimental reconstruction of the squared moduli \({\rho }_{ij}^{2}\) (red) and phases θij (blue) for three input ports of the reconfigurable photonic chip, highlighted by the labels in the figure. The chip is set on a random configuration of currents. Each input port represents a row of the unitary transformation applied to the input state. b, c Comparison of the phases and the squared moduli frequency distribution respectively, between 15 experimentally reconstructed sub-matrices (blue) and 15 [3 × 32] sub-matrices sampled from the Haar-random unitaries (red). d Distribution of the similarity between the squared moduli of two columns of different sub-matrices. We repeated the measurement for ~200 different configurations of the currents in the chip. In red it is shown the theoretical similarity distribution obtained by sampling columns distributed according to the Haar measure. The overlap between the two histograms is the 62.4% of the total area.
