A numerical model for time-multiplexed Ising machines based on delay-line oscillators

TL;DR

This paper models a time-multiplexed Ising machine using delay-line oscillators, analyzing how circuit parameters influence the probability of reaching the optimal solution, with implications for hardware-based NP-hard problem solving.

Contribution

The paper introduces a numerical model for delay-line oscillator-based Ising machines and studies parameter effects on solution optimality, demonstrating robustness across different network configurations.

Findings

Optimal parameter range near oscillator synchronization edge

High global minimum probability within specific parameter ranges

Sharp transition in solution quality related to circuit parameters

Abstract

Ising machines (IM) have recently been proposed as unconventional hardware-based computation accelerators for solving NP-hard problems. In this work, we present a model for a time-multiplexed IM based on the nonlinear oscillations in a delay line-based resonator and numerically study the effects that the circuit parameters, specifically the compression gain $\beta_r$ and frequency nonlinearity $\beta_i$, have on the IM solutions. We find that the likelihood of reaching the global minimum -- the global minimum probability (GMP) -- is the highest for a certain range of $\beta_r$ and $\beta_i$ located near the edge of the synchronization region of the oscillators. The optimal range remains unchanged for all tested coupling topologies and network connections. We also observe a sharp transition line in the ($\beta_i, \beta_r$) space above which the GMP falls to zero. In all cases, small variations in the natural frequency of the oscillators do not modify the results, allowing us to extend this model to realistic systems.