Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model

TL;DR

This paper proposes a nonstoquastic catalyst to enhance bifurcation-based quantum annealing, effectively eliminating first-order phase transitions in the ferromagnetic p-spin model and improving the energy gap scaling.

Contribution

The paper introduces a novel nonstoquastic catalyst for bifurcation-based quantum annealing, demonstrating its ability to prevent first-order phase transitions and improve energy gap scaling.

Findings

Eliminates first-order phase transition in the p-spin model

Energy gap decreases polynomially with system size with catalyst

Potential to significantly improve quantum annealing performance

Abstract

Introducing a nonstoquastic catalyst is a promising avenue to improve quantum annealing with the transverse field. In the present paper, we propose a nonstoquastic catalyst for bifurcation-based quantum annealing described by the spin-1 operators to improve the efficiency of a ground-state search. To investigate the effect of the nonstoquastic catalyst, we study the ferromagnetic $p$-spin model, which has difficulty with finding the ground state due to the first-order phase transition for quantum annealing. A semiclassical analysis shows that the problematic first-order phase transition can be eliminated by introducing the proposed nonstoquastic catalyst with the appropriate amplitude. We also numerically calculate the minimum energy gap for a finite-size system by diagonalizing the Hamiltonian. We find that while the energy gap decreases exponentially with increasing system size for the original Hamiltonian, it decreases polynomially against the system size for the Hamiltonian with the nonstoquastic catalyst. This result implies that the proposed nonstoquastic catalyst has the potential to improve the performance of bifurcation-based quantum annealing.