Fig. 2: Steps for Process Data.

Example experimental data and the processing neural network. a Example raw photon counts recorded by DD (direct detection) for the first image of digit “0", where each event counts photons for 100 μs, and there are 10 events for each DMD (digital micro-mirror device) pattern (thus the figure shows the results for 80 patterns). b Example raw photon counts recorded by QPMS (quantum parametric mode sorting) for the first image of digit “0", where each event counts photons for 40 μs, and there are 25 events for each DMD pattern (thus the figure shows the results for 80 patterns). c Example mean photon counts of QPMS for each DMD pattern by averaging over 20 of the 25 events, where the first three and last two events are dropped as the systems settle during the pattern transition. The effective integration time of photon counting is thus 0.8 millisecond in this case. Mean photon counts of DD for each DMD pattern by averaging over 8 of the 10 events, where the first and last events are dropped as the systems settle during the pattern transition. d The neural network architecture, used for the handwritten digit classification, consists of input, hidden, and output layers.