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

TL;DR

This paper demonstrates that the choice of nonlinear transfer function in analog Ising machines dramatically affects their computational efficiency and solution quality, with certain functions reducing amplitude inhomogeneity and enabling order-of-magnitude speedups.

Contribution

It shows how different nonlinear transfer functions influence performance and introduces saturation effects as a key factor in improving Ising machine efficiency.

Findings

Periodic, sigmoid, and clipped transfer functions significantly reduce calculation time.

Order-of-magnitude improvements in solution speed are achieved with certain nonlinearities.

Saturation of transfer functions suppresses amplitude inhomogeneity, enhancing performance.

Abstract

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 systems for building Ising machines and presents an efficient way for overcoming performance limitations.