Population annealing with topological defect driven nonlocal updates for spin systems with quenched disorder

Population annealing, one of the currently state-of-the-art algorithms for solving spin-glass systems, sometimes finds hard disorder instances for which its equilibration quality at each temperature step is severely damaged. In such cases, therefore, one cannot be sure about having reached the true ground state without vastly increasing the computational resources. In this work, we seek to overcome this problem by proposing a quantum-inspired modification of population annealing. Here we focus on the three-dimensional random plaquette gauge model, whose ground-state energy problem seems to be much harder to solve than that of the standard spin-glass Edwards-Anderson model. In analogy to the toric code, by allowing single bond flips we let the system explore nonphysical states, effectively expanding the configurational space by introducing topological defects that are then annealed through an additional field parameter. The dynamics of these defects allow for the effective realization of nonlocal cluster moves, potentially easing the equilibration process. We study the performance of this method in three-dimensional random plaquette gauge model lattices of various sizes, and we compare it against population annealing. With that we conclude that the newly introduced nonlocal moves are able to improve the equilibration of the lattices, in some cases being superior to a normal population annealing algorithm with a computational resource investment that is 16 times higher.