Multi-photon entanglement and interference are key in revealing strictly nonclassical phenomena. The generation of entangled photon pairs simply through laser-beam focusing onto a nonlinear optical crystal, along with single-photon manipulation and detection, has broad applications in fundamental quantum mechanics tests and innovative advancements including computation, communication and sensing. The progress in these areas benefits from the evolution of multi-channel multi-photon coincidence-measurement technologies that enable the characterization of spatial correlation and high-dimensional entanglement analysis. For instance, linear optical quantum computing relies on the coincidence detection of four paths and the ability to distinguish between zero, one and two photons. Moreover, photonic quantum walk and Boson sampling hinge on the coincidence detection of single or entangled photons across numerous spatial modes. Moving forwards, the realization of large-scale photonic circuits for these quantum optical experiments demands an increasing number of time-resolved single-photon detectors. Among the variety of single-photon detectors available, superconducting nanowire single-photon detectors (or SNSPDs) have gained prominence due to their outstanding performance metrics and potential for on-chip integration. However, traditional SNSPD arrays that are designed for few-channel coincidence counting with the parallel readout of individual detectors encounter significant hurdles when expanded to a large number of channels, particularly in terms of electrical readout.

Several multiplexing strategies have been explored to address the readout challenge, using methods such as row–column addressing and delay-time, amplitude and frequency multiplexing. Although the implementation format is already very large, these methods have focused primarily on determining the position of individual photons, and lack the capability to simultaneously measure multiple photons. This limitation arises because multi-photon coincidence detection in the array has an exponentially increased readout complexity with the number of photons and the indistinguishability of the multiplexed readout features. For example, amplitude multiplexing encodes the position and number of response pixels into the amplitude of the readout pulse, whose scalability is constrained by the signal-to-noise ratio of the pulse, thus the maximum number of pixels is only four so far. Traditional delay lines face challenges in determining the positions of two photons, often resulting in a false one-photon position located at the midpoint (xi + xj)/2 between the two photon locations xi and xj along the nanowire. Only a few device structures have attempted to achieve the simultaneous resolution of multi-photon positions for a large spatial mode by connecting all pixels in series with delay lines. Utilizing synchronous logic, single- and two-photon positions can be distinguished by jointly comparing the sum and difference of the pulse transmission time. However, this method cannot cope with the absence of a reference time, especially in scenarios such as photon-pair detection pumped by continuous light sources. On-chip inductors and resistors can also be connected in parallel for each pixel to facilitate rapid local current recovery after firing, which opens the transmission channel for the response pulse of multiple pixels. It is necessary, however, for adjacent pixels to provide a nanosecond-level delay time and entails the integration of large-format circuits and heterogeneous materials. Moreover, none of the current schemes can distinguish the photon number detected on a single pixel.

Here we introduce a two-photon coincidence counter based on superconducting nanowire transmission lines, referred to as a superconducting nanowire two-photon coincidence counter (SNTPC). In contrast to previous device architecture that uses uniform delay-line lengths, this coincidence counter topologically optimizes the delay-time series between adjacent pixels to distinguish the delay-time difference between pulse pairs from any one or two pixels. Utilizing combinatorial logic and amplitude multiplexing, we successfully showcase the ability to resolve all 152 possible single- and two-photon events in a 16-pixel device, including 16 single-photon cases, 120 cases of two photons hitting two different pixels 𝐶${16}_2^{}$and 16 cases of two photons on the same pixel. The SNTPC features an intrinsic self-coincidence counting capability, high scalability, streamlined fabrication processes, a straightforward two-terminal readout and the potential for waveguide integration, which are particularly suitable for two-photon coincidence detection in large-scale photonic integrated circuits.