Solving combinatorial optimization problems through stochastic Landau-Lifshitz-Gilbert dynamical systems

TL;DR

This paper introduces a novel approach for combinatorial optimization using physical dynamics of 3d rotors governed by Landau-Lifshitz-Gilbert equations, enabling escape from local minima and high-quality solutions.

Contribution

It proposes a physics-inspired optimization method leveraging macrospin dynamics, outperforming traditional relaxation techniques and compatible with magnetic device implementations.

Findings

Produces high-quality solutions comparable to state-of-the-art algorithms

Capable of escaping local minima through physical dynamics

Suitable for implementation with magnetic tunnel junction devices

Abstract

We present a method to approximately solve general instances of combinatorial optimization problems using the physical dynamics of 3d rotors obeying Landau-Lifshitz-Gilbert dynamics. Conventional techniques to solve discrete optimization problems that use simple continuous relaxation of the objective function followed by gradient descent minimization are inherently unable to avoid local optima, thus producing poor-quality solutions. Our method considers the physical dynamics of macrospins capable of escaping from local minima, thus facilitating the discovery of high-quality, nearly optimal solutions, as supported by extensive numerical simulations on a prototypical quadratic unconstrained binary optimization (QUBO) problem. Our method produces solutions that compare favorably with those obtained using state-of-the-art minimization algorithms (such as simulated annealing) while offering the advantage of being physically realizable by means of arrays of stochastic magnetic tunnel junction devices.