  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 if the shape of 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-ofmagnitude 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 systems for building Ising machines and presents an efficient
way for overcoming performance limitations.
