Fig. 4: Three photons in an eight-mode adaptive Boson Sampling interferometer for generating Gaussian kernels.
From: Quantum machine learning with Adaptive Boson Sampling via post-selection
a The [8, 3, 2, 15] ABS scheme of platform B2. We synchronize n = 3 photons emitted from the quantum dot source and we process them in the m = 8 mode universal integrated circuit. The optical circuit is divided into an 8-mode randomly extracted unitary U0 and a 2-mode adaptive unitary Ui. Triggered by the detection of r = 2 photons in the 6 adaptive modes oj, the reflectivity value of the beam-splitter θi assumes 15 different values allowing for the reconstruction of 15 × 15 kernels. The green part of the circuit highlights the tomography station in which the dual rail qubit encoded in the remaining photon conditioned on the detection of the r photons in the other oj outputs is analyzed. On the right panel, we report the comparison between the 15 × 15 kernel simulated according to the theoretical model and the experimental one. b The [8, 3, 3, 15] scheme that encodes classical data in qutrit states (platform B3). The 8-mode U0 is followed by 3-mode adaptive Ui in which the reflectivity of two beam-splitters has been properly programmed in order to implement 15 different unitaries as before. Triggering on the detection of r = 2 photons in the 5 adaptive modes oj, considering both configurations in which photons are bunched in the same mode or are output from different modes, a 15 × 15 kernel has been reconstructed. The green part of the circuit is again the tomography station that analyzes the three-rail qutrit. The right panel reports the comparison between the 15 × 15 kernel simulated according to the theoretical model and the experimental one. c Experimental ρi density matrices for qutrits ρ1 and ρ2 to which correspond the following fidelity with the expected theoretical state, F1 = 0.995 ± 0.001 and F2 = 0.953 ± 0.010. The experimental density matrices are reconstructed by measuring in the tomography stage the generalized Pauli operators. Both experiments reported here were carried out with SNSPDs.
