Dynamics of simulated quantum annealing in random Ising chains
Glen Bigan Mbeng, Lorenzo Privitera, Luca Arceci, Giuseppe E. Santoro · Physical review. B./Physical review. B · 2019
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 ${\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{QA}}\ensuremath{\sim}{({log}_{10}\ensuremath{\tau})}^{\ensuremath{-}2}$ as opposed to ${\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{SA}}\ensuremath{\sim}{({log}_{10}\ensuremath{\tau})}^{\ensuremath{-}1}, \ensuremath{\tau}$ being the total annealing time, while for the ordered case both give the same power law ${\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{QA}}\ensuremath{\approx}{\ensuremath{\rho}}_{\mathrm{KZ}}^{\mathrm{SA}}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$. We show that the dynamics of SQA, while correctly capturing the Kibble-Zurek scaling ${\ensuremath{\tau}}^{\ensuremath{-}1/2}$ for the ordered case, is unable to reproduce the QA dynamics in the disordered case at intermediate $\ensuremath{\tau}$. 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.