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Recently, Heim, Ronnow, Isakov and Troyer [Science 348 (2015) 215] havereported that Monte Carlo simulations for the Ising spin glass model on thesquare lattice in the physically relevant continuous-imaginary-time limit donot show superiority of quantum annealing (QA) using transverse field againstclassical annealing (CA). Although the QA schedule that they had used has beenusing conventionally, however the QA schedule mathematically has no guaranteethat the used schedule is the best QA schedule for performance of optimization.We propose a new QA schedule for studying transverse-field-based quantum versusclassical annealing of the Ising model. The present QA schedule utilizes asmallest effective transverse field derived in this article. This QA scheduleis made for the comparison between the system with no transverse field and thesystem with the smallest effective transverse field. As a case study, we studyQA of the Ising spin glass model on the square lattice at low but finitetemperature. A Monte Carlo algorithm using the physically relevantcontinuous-imaginary-time limit is performed. As the simulation results, weshow superiority of QA against CA when the annealing time is sufficientlyspent.

Proposal of a new quantum annealing schedule for studying quantum annealing of transverse field Ising models