Quantum annealing with antiferromagnetic fluctuations

TL;DR

This paper proposes adding antiferromagnetic quantum fluctuations to quantum annealing, demonstrating through analysis and simulations that it can avoid first-order transitions and efficiently find ground states in certain models.

Contribution

It introduces a novel quantum annealing approach with antiferromagnetic fluctuations and shows it can bypass first-order transitions in the p-spin model.

Findings

Avoids first-order transitions for intermediate p values

Energy gap scales polynomially at second-order transitions

Potential for efficient quantum annealing in specific models

Abstract

We introduce antiferromagnetic quantum fluctuations into quantum annealing in addition to the conventional transverse-field term. We apply this method to the infinite-range ferromagnetic p-spin model, for which the conventional quantum annealing has been shown to have difficulties to find the ground state efficiently due to a first-order transition. We study the phase diagram of this system both analytically and numerically. Using the static approximation, we find that there exists a quantum path to reach the final ground state from the trivial initial state that avoids first-order transitions for intermediate values of p. We also study numerically the energy gap between the ground state and the first excited state and find evidence for intermediate values of p that the time complexity scales polynomially with the system size at a second-order transition point along the quantum path that avoids first-order transitions. These results suggest that quantum annealing would be able to solve this problem with intermediate values of p efficiently in contrast to the case with only simple transverse-field fluctuations.