Stochastic matrix multiplier using superconductor single-flux-quantum circuit

A superconducting single-flux-quantum (SFQ) circuit is suitable for stochastic computation that represents information in terms of the probability of '1's in a finite-bit-length number train, due to its high-speed operation. In this paper, we demonstrate a matrix multiplier based on the SFQ logic circuits and superconductive random number generators (SRNGs). The stochastic multiplier required for the matrix product calculation is implemented using an AND gate. The stochastic adder is implemented by a multiplexer where the random number train generated by the SRNG is utilized as a control signal. We implemented 2x2 matrix multiplier targeting a frequency of 50 GHz, using the 10 kA cm-2 Nb 4-layer superconductor circuit fabrication process. Numerical calculation results show that the designed stochastic matrix multiplier can multiply with a computational error of 1.12% when the input stochastic numbers are 1000-bit number trains. In the measurements, the input stochastic numbers were also generated by SRNGs, and the operation of the test circuit was verified. We experimentally demonstrated the correct operation of the matrix multiplier, and the obtained calculation errors agreed with theoretical values. To the best of our knowledge, this is the first demonstration of stochastic arithmetic operation using SFQ circuits.