Relation between quantum fluctuations and the performance enhancement of quantum annealing in a nonstoquastic Hamiltonian

TL;DR

This paper investigates how quantum fluctuations influence the performance of quantum annealing in a mean-field Hamiltonian, revealing that quantum effects are more prominent around second-order phase transitions, which correlates with performance enhancement.

Contribution

It demonstrates that antiferromagnetic transverse interactions induce quantum effects mainly near second-order transitions, explaining the performance boost in quantum annealing.

Findings

Quantum fluctuations are significant around second-order transitions.

Quantum effects are less prominent at first-order transitions.

Quantum fluctuations are large within the ferromagnetic phase after a second-order transition.

Abstract

We study the relation between quantum fluctuations and the significant enhancement of the performance of quantum annealing in a mean-field Hamiltonian. First-order quantum phase transitions were shown to be reduced to second order by antiferromagnetic transverse interactions in a mean-field-type many-body-interacting Ising spin system in a transverse field, which means an exponential speedup of quantum annealing by adiabatic quantum computation. We investigate if and how quantum effects manifest themselves around these first- and second-order phase transitions to understand if the antiferromagnetic transverse interactions appended to the conventional transverse-field Ising model induce notable quantum effects. By measuring the proximity of the semiclassical spin-coherent state to the true ground state as well as the magnitude of the concurrence representing entanglement, we conclude that significant quantum fluctuations exist around second-order transitions, whereas quantum effects are much less prominent at first-order transitions. Although the location of the transition point can be predicted by the classical picture, system properties near the transition need quantum-mechanical descriptions for a second-order transition but not necessarily for first order. It is also found that quantum fluctuations are large within the ferromagnetic phase after a second-order transition from the paramagnetic phase. These results suggest that the antiferromagnetic transverse interactions induce marked quantum effects, and this fact would be related to closely to the significant enhancement of the performance of quantum annealing.