  Photon number resolving (PNR) is an important capacity for detectors working
in quantum and classical applications. Although a conventional superconducting
nanowire single-photon detector (SNSPD) is not a PNR detector, by arranging
nanowires in a series array and multiplexing photons over space, such series
PNR-SNSPD can gain quasi-PNR capacity. However, the accuracy and maximum
resolved photon number are both limited by the signal-to-noise (SNR) ratio of
the output pulses. Here, we introduce a matched filter, which is an optimal
filter in terms of SNR for SNSPD pulses. Experimentally, compared to
conventional readout using a room-temperature amplifier, the normalized spacing
between pulse amplitudes from adjacent photon number detections increased by a
maximum factor of 2.1 after the matched filter. Combining with a cryogenic
amplifier to increase SNR further, such spacing increased by a maximum factor
of 5.3. In contrast to a low pass filter, the matched filter gave better SNRs
while maintaining good timing jitters. Minimum timing jitter of 55 ps was
obtained experimentally. Our results suggest that the matched filter is a
useful tool for improving the performance of the series PNR-SNSPD and the
maximum resolved photon number can be expected to reach 65 or even large.
