论文标题
基于分叉的非序列催化剂基于分叉的量子退火$ p $ -spin型号
Nonstoquastic catalyst for bifurcation-based quantum annealing of ferromagnetic $p$-spin model
论文作者
论文摘要
引入非论序催化剂是通过横向场改善量子退火的有前途的途径。在本文中，我们提出了一种非常规催化剂，用于基于分叉的量子退火，由Spin-1操作员提高地面搜索的效率。为了研究非论序催化剂的效果，我们研究了铁磁$ p $ -spin模型，由于量子退火的一阶相变，该模型很难找到基态。半经典分析表明，可以通过以适当的幅度引入所提出的非论序催化剂来消除有问题的一阶相变。我们还通过对将哈密顿量对角线化来计算有限大小系统的最小能隙。我们发现，虽然能量差距随着原始哈密顿量的系统尺寸的增加而呈指数降低，但使用非论奎斯特催化剂的哈密顿量对哈密顿量的系统大小降低。该结果意味着所提出的非阶级催化剂有可能提高基于分叉的量子退火的性能。
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.
