  Recently, Heim, Ronnow, Isakov and Troyer [Science 348 (2015) 215] have
reported that Monte Carlo simulations for the Ising spin glass model on the
square lattice in the physically relevant continuous-imaginary-time limit do
not show superiority of quantum annealing (QA) using transverse field against
classical annealing (CA). Although the QA schedule that they had used has been
using conventionally, however the QA schedule mathematically has no guarantee
that the used schedule is the best QA schedule for performance of optimization.
We propose a new QA schedule for studying transverse-field-based quantum versus
classical annealing of the Ising model. The present QA schedule utilizes a
smallest effective transverse field derived in this article. This QA schedule
is made for the comparison between the system with no transverse field and the
system with the smallest effective transverse field. As a case study, we study
QA of the Ising spin glass model on the square lattice at low but finite
temperature. A Monte Carlo algorithm using the physically relevant
continuous-imaginary-time limit is performed. As the simulation results, we
show superiority of QA against CA when the annealing time is sufficiently
spent.
