Can nonlinear parametric oscillators solve random Ising models?

TL;DR

This paper investigates the capability of large networks of nonlinear parametric oscillators, known as coherent Ising machines, to solve random Ising models, revealing that nonlinearities above threshold improve solution accuracy.

Contribution

The study demonstrates that nonlinear parametric oscillator networks can effectively find Ising ground states when driven sufficiently above threshold, challenging previous assumptions.

Findings

Networks converge to Ising ground states with finite probability

Nonlinearities are crucial for the network to find correct solutions

Most-efficient mode does not always match the Ising ground state

Abstract

We study large networks of parametric oscillators as heuristic solvers of random Ising models. In these networks, known as coherent Ising machines, the model to be solved is encoded in the coupling between the oscillators, and a solution is offered by the steady state of the network. This approach relies on the assumption that mode competition steers the network to the ground-state solution of the Ising model. By considering a broad family of frustrated Ising models, we show that the most-efficient mode does not correspond generically to the ground state of the Ising model. We infer that networks of parametric oscillators close to threshold are intrinsically not Ising solvers. Nevertheless, the network can find the correct solution if the oscillators are driven sufficiently above threshold, in a regime where nonlinearities play a predominant role. We find that for all probed instances of the model, the network converges to the ground state of the Ising model with a finite probability.