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We demonstrate the operation of a coincidence photon detector with a short timing jitter consisting of two superconducting nanowire single photon detectors (SSPDs) and a single flux quantum (SFQ) circuit. By utilizing the timing discrimination capability of the SFQ coincidence circuit, the full width at half maximum timing jitter of the entire coincidence photon detector was evaluated as 32.3 ps, which is 36 ps less than that of the standard commercial time correlated single photon counting module, and the timing jitter of the SSPD was estimated as ∼15 ps. Owing to the short timing jitter characteristics, our coincidence photon detector could correctly capture the effect of pulse-width broadening by insertion of an optical bandpass filter. We have also demonstrated that our coincidence photon detection clearly shows Hong-Ou-Mandel interference with a weak coherent pulse. These results are a crucial step to realizing high timing resolution coincidence measurements, ushering in a technology for timing measurement based multi-photon quantum interference. [ABSTRACT FROM AUTHOR]