Quantum annealing of an Ising spin-glass by Green's function Monte Carlo

TL;DR

This paper explores quantum annealing using Green's function Monte Carlo for Ising spin-glasses, comparing its effectiveness to Path-Integral Monte Carlo and classical methods, and finds it currently less efficient without better importance sampling.

Contribution

It introduces a GFMC-based quantum annealing approach for spin-glasses and analyzes the impact of trial wavefunctions on its performance.

Findings

GFMC-QA results are similar to classical annealing but more computationally intensive.

GFMC-QA performs worse than PIMC-QA in current implementations.

Importance sampling with good trial wavefunctions is crucial for GFMC-QA effectiveness.

Abstract

We present an implementation of Quantum Annealing (QA) via lattice Green's function Monte Carlo (GFMC), focusing on its application to the Ising spin-glass in transverse field. In particular, we study whether or not such method is more effective than the Path-Integral Monte Carlo (PIMC) based QA, as well as classical simulated annealing (CA), previously tested on the same optimization problem. We identify the issue of importance sampling, i.e., the necessity of possessing reasonably good (variational) trial wavefunctions, as the key point of the algorithm. We have considered two possible classes of trial wavefunctions, a mean-field single-site one -- whose optimization is however a very difficult task -- and a Boltzmann-like choice. We performed GFMC-QA runs using such a Boltzmann-like trial wavefunction, finding results for the residual energies that are qualitatively similar to those of CA (but at a much larger computational cost), and definitely worse than PIMC-QA. We conclude that, at present, without a serious effort in constructing reliable importance sampling variational wavefunctions for a quantum glass, GFMC-QA is not a true competitor of PIMC-QA.