Order-of-magnitude differences in computational performance of analog Ising machines induced by the choice of nonlinearity

Analog Ising machines are promising fast computing schemes for some difficult optimization problems, yet their analog nature is known to cause errors and inhibit computational performance. Here, the authors investigate how the choice of nonlinear transfer functions partly suppresses errors caused by analog amplitude inhomogeneity, which leads to order-of-magnitude differences in the computation time. Ising machines based on nonlinear analog systems are a promising method to accelerate computation of NP-hard optimization problems. Yet, their analog nature is also causing amplitude inhomogeneity which can deteriorate the ability to find optimal solutions. Here, we investigate how the system's nonlinear transfer function can mitigate amplitude inhomogeneity and improve computational performance. By simulating Ising machines with polynomial, periodic, sigmoid and clipped transfer functions and benchmarking them with MaxCut optimization problems, we find the choice of transfer function to have a significant influence on the calculation time and solution quality. For periodic, sigmoid and clipped transfer functions, we report order-of-magnitude improvements in the time-to-solution compared to conventional polynomial models, which we link to the suppression of amplitude inhomogeneity induced by saturation of the transfer function. This provides insights into the suitability of nonlinear systems for building Ising machines and presents an efficient way for overcoming performance limitations.