Theory of Quantum Annealing of an Ising Spin Glass

TL;DR

This paper demonstrates the effectiveness of quantum annealing over classical methods in finding low-energy states of an Ising spin glass, supported by a new theoretical framework based on Landau-Zener tunneling.

Contribution

It introduces a theory of quantum annealing using Landau-Zener tunneling events and compares its performance to classical annealing on a 2D Ising model.

Findings

Quantum annealing outperforms classical annealing in energy minimization.

Residual energy decreases as a power of the logarithm of annealing time, faster in quantum case.

Proposed theory explains quantum annealing dynamics through cascade tunneling events.

Abstract

Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. Comparing classical and quantum Monte Carlo annealing protocols on the random two-dimensional Ising model we confirm the superiority of quantum annealing relative to classical annealing. We also propose a theory of quantum annealing, based on a cascade of Landau-Zener tunneling events. For both classical and quantum annealing, the residual energy after annealing is inversely proportional to a power of the logarithm of the annealing time, but the quantum case has a larger power which makes it faster