Ising machines as hardware solvers of combinatorial optimization problems

TL;DR

This review discusses various hardware implementations of Ising machines, their operational principles, performance metrics, and potential to efficiently solve complex combinatorial optimization problems by finding ground states of the Ising model.

Contribution

It provides a comprehensive comparison of classical, quantum, and hybrid Ising machine approaches, highlighting their advantages, limitations, and scalability for practical optimization tasks.

Findings

Superconducting quantum annealers show promising scalability.

Optical Ising machines achieve high success probabilities.

Classical hardware accelerators outperform some quantum approaches in certain metrics.

Abstract

Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity class NP as an Ising problem with only polynomial overhead. A scalable Ising machine that outperforms existing standard digital computers could have a huge impact for practical applications for a wide variety of optimization problems. In this review, we survey the current status of various approaches to constructing Ising machines and explain their underlying operational principles. The types of Ising machines considered here include classical thermal annealers based on technologies such as spintronics, optics, memristors, and digital hardware accelerators; dynamical-systems solvers implemented with optics and electronics; and superconducting-circuit quantum annealers. We compare and contrast their performance using standard metrics such as the ground-state success probability and time-to-solution, give their scaling relations with problem size, and discuss their strengths and weaknesses.