  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 one can therefore not 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 three-dimensional random plaquette gauge
model which ground state energy problem seems to be much harder to solve than
standard spin-glass Edwards-Anderson model. In analogy to the Toric Code, by
allowing single bond flips we let the system explore non-physical states,
effectively expanding the configurational space by the introduction of
topological defects that are then annealed through an additional field
parameter. The dynamics of these defects allow for the effective realization of
non-local cluster moves, potentially easing the equilibration process. We study
the performance of this new method in three-dimensional random plaquette gauge
model lattices of various sizes and compare it against Population Annealing.
With that we conclude that the newly introduced non-local moves are able to
improve the equilibration of the lattices, in some cases being superior to a
normal Population Annealing algorithm with a sixteen times higher computational
resource investment.
