Efficient sampling of ground and low-energy Ising spin configurations with a coherent Ising machine

TL;DR

This paper demonstrates that a measurement-feedback-based coherent Ising machine can efficiently sample low-energy spin configurations in the presence of quantum noise, outperforming traditional models especially in low-finesse regimes, with promising applications for solving MAX-CUT problems.

Contribution

The authors develop a discrete-time Gaussian-state model of the MFB-CIM that accurately captures nonlinear quantum dynamics and shows improved sampling efficiency in low-finesse regimes compared to existing models.

Findings

Sampling time scales as 1.08^N for MAX-CUT problems.

Median sampling time of 6 million roundtrips for N=100.

Sampling performance is robust to drive sign reversal and depends critically on optical nonlinearity.

Abstract

We show that the nonlinear stochastic dynamics of a measurement-feedback-based coherent Ising machine (MFB-CIM) in the presence of quantum noise can be exploited to sample degenerate ground and low-energy spin configurations of the Ising model. We formulate a general discrete-time Gaussian-state model of the MFB-CIM which faithfully captures the nonlinear dynamics present at and above system threshold. This model overcomes the limitations of both mean-field models, which neglect quantum noise, and continuous-time models, which assume long photon lifetimes. Numerical simulations of our model show that when the MFB-CIM is operated in a quantum-noise-dominated regime with short photon lifetimes (i.e., low cavity finesse), homodyne monitoring of the system can efficiently produce samples of low-energy Ising spin configurations, requiring many fewer roundtrips to sample than suggested by established high-finesse, continuous-time models. We find that sampling performance is robust to, or even improved by, turning off or altogether reversing the sign of the parametric drive, but performance is critically reduced in the absence of optical nonlinearity. For the class of MAX-CUT problems with binary-signed edge weights, the number of roundtrips sufficient to fully sample all spin configurations up to the first-excited Ising energy, including all degeneracies, scales as $1.08^N$. At a problem size of $N = 100$ with a few dozen (median of 20) such desired configurations per instance, we have found median sufficient sampling times of $6\times10^6$ roundtrips; in an experimental implementation of an MFB-CIM with a 10 GHz repetition rate, this corresponds to a wall-clock sampling time of 60 ms.