Solving combinatorial optimization problems through stochastic Landau-Lifshitz-Gilbert dynamical systems
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.
Cite
@article{arxiv.2407.00530,
title = {Solving combinatorial optimization problems through stochastic Landau-Lifshitz-Gilbert dynamical systems},
author = {Dairong Chen and Andrew D. Kent and Dries Sels and Flaviano Morone},
journal= {arXiv preprint arXiv:2407.00530},
year = {2025}
}