Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs

TL;DR

This paper compares quantum and classical annealing in a spin glass model on 3-regular graphs, finding quantum annealing less efficient than classical methods for reaching the glass phase based on critical scaling analysis.

Contribution

It provides a detailed comparison of quantum and classical annealing efficiency using out-of-equilibrium quantum Monte Carlo simulations and critical scaling analysis.

Findings

Quantum annealing is less efficient than classical simulated annealing for this spin glass model.

Critical exponents differ between quantum and classical transitions, indicating different universality classes.

Quantum computing based on quantum annealing may be inferior for certain glassy problems.

Abstract

We discuss an Ising spin glass where each $S=1/2$ spin is coupled antiferromagnetically to three other spins (3-regular graphs). Inducing quantum fluctuations by a time-dependent transverse field, we use out-of-equilibrium quantum Monte Carlo simulations to study dynamic scaling at the quantum glass transition. Comparing the dynamic exponent and other critical exponents with those of the classical (temperature-driven) transition, we conclude that quantum annealing is less efficient than classical simulated annealing in bringing the system into the glass phase. Quantum computing based on the quantum annealing paradigm is therefore inferior to classical simulated annealing for this class of problems. We also comment on previous simulations where a parameter is changed with the simulation time, which is very different from the true Hamiltonian dynamics simulated here.