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

• URL: http://arxiv.org/abs/2209.01737v2
• Date: Mon, 8 May 2023 01:39:46 GMT
• Title: Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model
• Authors: Yuki Susa, Takashi Imoto, Yuichiro Matsuzaki
• Abstract summary: We propose a nonstoquastic catalyst to improve the efficiency of a ground-state search. A semiclassical analysis shows that the problematic first-order phase transition can be eliminated. We find that while the energy gap decreases with increasing system size for the original Hamiltonian, it decreases exponentially against the system size for the Hamiltonian with the nonstoquastic catalyst.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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