Experimental investigation of performance differences between Coherent Ising Machines and a quantum annealer

TL;DR

This study compares the performance of D-Wave quantum annealers and coherent Ising machines (CIMs) on NP-hard problems, revealing that CIMs outperform quantum annealers on denser problem instances, highlighting the importance of connectivity.

Contribution

It provides the first detailed experimental comparison between quantum annealers and CIMs on large, dense Ising problems, emphasizing the impact of connectivity on performance.

Findings

CIMs outperform D-Wave on dense MAX-CUT problems.

Quantum annealer's performance degrades exponentially with problem size.

Connectivity differences significantly affect annealer performance.

Abstract

Physical annealing systems provide heuristic approaches to solving NP-hard Ising optimization problems. Here, we study the performance of two types of annealing machines--a commercially available quantum annealer built by D-Wave Systems, and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillator networks--on two classes of problems, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on regular graphs of degree 3. On denser problems, however, we observe an exponential penalty for the quantum annealer ($\exp(-\alpha_\textrm{DW} N^2)$) relative to CIMs ($\exp(-\alpha_\textrm{CIM} N)$) for fixed anneal times, on both the SK model and on 50%-edge-density MAX-CUT, where the coefficients $\alpha_\textrm{CIM}$ and $\alpha_\textrm{DW}$ are problem-class-dependent. On instances with over $50$ vertices, a several-orders-of-magnitude time-to-solution difference exists between CIMs and the D-Wave annealer. An optimal-annealing-time analysis is also consistent with a significant projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the measurement-feedback facilitated all-to-all connectivity of the CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.