Quantum Annealing in SK Model Employing Suzuki-Kubo-deGennes Quantum Ising Mean Field Dynamics

TL;DR

This paper introduces a quantum annealing method using Suzuki-Kubo-deGennes dynamics to efficiently estimate the ground state energy of the SK spin glass model, achieving results close to the best known estimates.

Contribution

It presents a novel quantum annealing algorithm based on coupled differential equations for local magnetizations, offering a fast and accurate approach for the SK model.

Findings

Estimated ground state energies closely match known values.

The method avoids the de-Almeida-Thouless line due to continuous magnetization variables.

The algorithm has a computational cost of approximately N^3.

Abstract

We study a quantum annealing approach for estimating the ground state energy of the Sherrington-Kirpatrick mean field spin glass model using the Suzuki-Kubo-deGennes dynamics applied for individual local magnetization components. The solutions of the coupled differential equations, in discretized state, give a fast annealing algorithm (cost $N^3$) in estimating the ground state of the model: Classical ($E^0= -0.7629 \pm 0.0002$), Quantum ($E^0=-0.7623 \pm 0.0001$) and Mixed ($E^0=-0.7626 \pm 0.0001$), all of which are to be compared with the best known estimate $E^0= -0.763166726 \dots$ . We infer that the continuous nature of the magnetization variable used in the dynamics here is the reason for reaching close to the ground state quickly and also the reason for not observing the de-Almeida-Thouless line in this approach.