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.

基于非线性模拟系统的伊辛机是加速 NP-hard 优化问题计算的一种很有前途的方法。然而，它们的模拟性质也导致幅度不均匀，这会降低找到最佳解决方案的能力。在这里，我们研究了系统的非线性传递函数如何减轻幅度不均匀性并提高计算性能。通过使用多项式、周期、sigmoid 和剪裁传递函数模拟 Ising 机器，并使用 MaxCut 优化问题对它们进行基准测试，我们发现传递函数的选择对计算时间和求解质量有显着影响。对于周期性、sigmoid 和限幅传递函数，我们报告了与传统多项式模型相比，求解时间的数量级改进，我们将其与抑制传递函数饱和引起的幅度不均匀性联系起来。这为构建伊辛机器的非线性系统的适用性提供了见解，并提供了克服性能限制的有效方法。