Quantum Annealing in the Transverse Ising Model

TL;DR

This paper explores quantum annealing using the transverse Ising model, demonstrating that quantum fluctuations can more effectively find ground states than classical thermal methods in small systems.

Contribution

It introduces a quantum annealing approach with a time-dependent transverse field and compares its effectiveness to classical simulated annealing.

Findings

Quantum annealing achieves higher ground state probabilities.

Quantum approach outperforms classical thermal methods in tested cases.

Abstract

We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between states and thus play the same role as thermal fluctuations in the conventional approach. The idea is tested by the transverse Ising model, in which the transverse field is a function of time similar to the temperature in the conventional method. The goal is to find the ground state of the diagonal part of the Hamiltonian with high accuracy as quickly as possible. We have solved the time-dependent Schr\"odinger equation numerically for small size systems with various exchange interactions. Comparison with the results of the corresponding classical (thermal) method reveals that the quantum annealing leads to the ground state with much larger probability in almost all cases if we use the same annealing schedule.