Optimization in random field Ising models by quantum annealing

TL;DR

This study explores how quantum annealing optimizes the random field Ising model across different dimensions, revealing phase-dependent decay rates of residual energy and the impact of cluster size on optimization difficulty.

Contribution

It provides new insights into the decay behavior of residual energy in quantum annealing for RFIM and how phase and cluster size influence optimization efficiency.

Findings

Residual energy decay follows a logarithmic power law with exponent $_{res} o ext{log}(N_{MC})^{-}$.

Ordered phase exhibits a decay exponent of 2, while paramagnetic phase can reach up to 6.

Large clusters increase the difficulty of optimization as indicated by lower decay exponents.

Abstract

We investigate the properties of quantum annealing applied to the random field Ising model in one, two and three dimensions. The decay rate of the residual energy, defined as the energy excess from the ground state, is find to be $e_{res}\sim \log(N_{MC})^{-\zeta}$ with $\zeta$ in the range $2...6$, depending on the strength of the random field. Systems with ``large clusters'' are harder to optimize as measured by $\zeta$. Our numerical results suggest that in the ordered phase $\zeta=2$ whereas in the paramagnetic phase the annealing procedure can be tuned so that $\zeta\to6$.