We study the performance of quantum annealing for two sets of problems, namely, 2-satisfiability (2-SAT) problems represented by Ising-type Hamiltonians and nonstoquastic problems which are obtained by adding extra couplings to the 2-SAT problem Hamiltonians. In addition, we add to the transverse Ising-type Hamiltonian used for quantum annealing a third term, the trigger Hamiltonian with ferromagnetic or antiferromagnetic couplings, which vanishes at the beginning and end of the annealing process. We also analyze some problem instances using the energy spectrum, average energy or overlap of the state during the evolution with the instantaneous low-lying eigenstates of the Hamiltonian, and identify some nonadiabatic mechanisms which can enhance the performance of quantum annealing.

中文翻译：

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触发哈密顿量的量子退火：在 2-可满足性和非稳态问题中的应用

我们研究了量子退火对两组问题的性能，即由伊辛型哈密顿量表示的 2-可满足性 (2-SAT) 问题和通过向 2-SAT 问题哈密顿量添加额外耦合获得的非稳态问题。此外，我们在用于量子退火的横向 Ising 型哈密顿量中添加了第三项，即具有铁磁或反铁磁耦合的触发哈密顿量，它在退火过程的开始和结束时消失。我们还利用演化过程中的能谱、平均能量或状态与哈密顿量瞬时低本征态的重叠分析了一些问题实例，并确定了一些可以提高量子退火性能的非绝热机制。