Time-multiplexed optoelectronic parametric oscillators with increased clock-rates toward Ising machine

Coherent Ising machines (CIMs) provide a heuristic approach to solving combinatorial optimization problems. As a physical annealing system, CIMs show considerable promise for outperforming digital computers in terms of the time required to obtain good approximate solutions, particularly for large-scale problems. However, due to the limitations imposed by the bandwidth and non-flat RF-to-IF response of electrical mixers, the clock-rate of CIMs based on an optoelectronic parametric oscillator (OEPO) is significantly lower than that of other implementations. In this paper, we propose employing a Mach-Zehnder modulator (MZM) as the nonlinear element in the loop, which enables the clock rate of time-multiplexed OEPOs to reach 1 GHz while critically maintaining spin independence. The proposed system generates 24,420 spins using approximately 5 km of optical fiber. A proof-of-concept experiment was conducted to demonstrate the independence and long-term stability of spins in the no-interaction system, as further evidenced by the binary sequences generated by the OEPOs successfully passing the NIST random number test. This advancement paves the way for the development of large-scale analog Ising machines as commercial combinatorial optimization solvers.