Simulated quantum annealing (SQA) is a classical computational strategy that emulates a quantum annealing (QA) dynamics through a path-integral Monte Carlo whose parameters are changed during the simulation. Here we apply SQA to the one-dimensional transverse field Ising chain, where previous works have shown that, in the presence of disorder, a coherent QA provides a quadratic speedup with respect to classical simulated annealing, with a density of Kibble-Zurek defects decaying as ρKZQA∼(log10τ)-2 as opposed to ρKZSA∼(log10τ)-1, τ being the total annealing time, while for the ordered case both give the same power law ρKZQA≈ρKZSA∼τ-1/2. We show that the dynamics of SQA, while correctly capturing the Kibble-Zurek scaling τ-1/2 for the ordered case, is unable to reproduce the QA dynamics in the disordered case at intermediate τ. We analyze and discuss several issues related to the choice of the Monte Carlo moves (local or global in space), the time-continuum limit needed to eliminate the Trotter-discretization error, and the long autocorrelation times shown by a local-in-space Monte Carlo dynamics for large disordered samples.
