Simulated quantum annealing of double-well and multi-well potentials

TL;DR

This paper compares quantum annealing methods with classical annealing for optimizing complex potential landscapes, showing that projective quantum Monte Carlo remains effective where classical methods falter.

Contribution

It demonstrates the superior performance of projective quantum Monte Carlo over finite-temperature QMC and classical annealing in complex optimization landscapes.

Findings

Projective QMC outperforms finite-temperature QMC.

Classical annealing is more efficient with long-range moves.

Projective QMC remains stable as problem complexity increases.

Abstract

We analyze the performance of quantum annealing as a heuristic optimization method to find the absolute minimum of various continuous models, including landscapes with only two wells and also models with many competing minima and with disorder. The simulations performed using a projective quantum Monte Carlo (QMC) algorithm are compared with those based on the finite-temperature path-integral QMC technique and with classical annealing. We show that the projective QMC algorithm is more efficient than the finite-temperature QMC technique, and that both are inferior to classical annealing if this is performed with appropriate long-range moves. However, as the difficulty of the optimization problem increases, classical annealing looses efficiency, while the projective QMC algorithm keeps stable performance and is finally the most effective optimization tool. We discuss the implications of our results for the outstanding problem of testing the efficiency of adiabatic quantum computers using stochastic simulations performed on classical computers.