  It has recently been shown that optical parametric oscillator (OPO) Ising
machines, consisting of coupled optical pulses circulating in a cavity with
parametric gain, can be used to probabilistically find low-energy states of
Ising spin systems. In this work, we study optical Ising machines that operate
under simplified Gaussian dynamics. We show that these dynamics are sufficient
for reaching probabilities of success comparable to previous work. Based on
this result, we propose modified optical Ising machines with simpler designs
that do not use parametric gain yet achieve similar performance, thus
suggesting a route to building much larger systems.
