发表机构
Nissin-Sumiden Energy System R&D Center Sumitomo Electric Industries, Ltd.（住友电气工业有限公司日电Sumiden能源系统研发中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出嵌套模拟退火（NSA）方法，推导相关能量计算公式，明确局部极大值与收敛速度的关系，证明合理选择NSA参数可实现高效绝热相变，为经典计算机模拟QMC提供参数选择方法。
AI 中文摘要
量子退火（QA）已投入实际应用，被认为可用于解决诸多社会问题，如减少交通拥堵和优化配送。但在QA中，当基态与第一激发态之间的能量差较小时，二者间的跃迁概率会增大，因此为降低跃迁，QA必须在极低温度下运行，而模拟该情况会耗费大量时间。目前多项研究正从理论层面加速QA，其中之一是引入非随机哈密顿量。另一方面，本文作者受量子蒙特卡洛（QMC）启发提出了嵌套模拟退火（NSA），通过优先考虑自旋翻转效应仅影响与其直接相互作用的自旋这一思路，证明其可实现显著的计算加速。尽管NSA基于经典因果关系概念，但量子与经典方法的混合计算效果良好。本文为探讨NSA与XX相互作用等非随机哈密顿量的关系，将自旋视为连续变量，推导了计算问题哈密顿量及横向电磁场诱导的微扰哈密顿量总能量的公式，并将展示用二元自旋计算时局部极大值与收敛速度的明确关系：更准确地说，即使消耗更少计算资源，具有最小局部极大值的退火路径也能快速收敛。因此，通过适当选择NSA参数可诱导最优绝热相变，本文提出了在经典计算机上模拟QMC时选择参数的有效方法。
英文摘要
Quantum Annealing (QA) has already put into practical use and considered useful for solving many social issues, such as reduction of traffic congestion and delivery optimization. But in QA, when the energy difference between the ground state and the first excited state is small, the transition probability between them increases. Therefore, in order to decrease the transition, QA has to be performed at extremely low temperatures. To simulate the situation, it has the problem in that it takes much time. Many studies are underway to accelerate QA theoretically, one of which is to incorporate non-stoquastic Hamiltonian. On the other hand, I proposed Nested Simulated Annealing (NSA) inspired by Quantum Monte Carlo (QMC). I showed the computational speedup could be achieved dramatically, by considering the idea that the effect of flipping a spin preferentially influenced the spins directly interacting with it. Although NSA was based on such classical concept of causality, the hybrid computation both quantum and classical approach worked well. In this paper, in order to discuss the relationship between NSA and non-stoquastic Hamiltonian like XX-interaction, the spins are treated as continuous variables. I derive the formula to calculate the total energy in both with a problem Hamiltonian and the perturbation Hamiltonian induced by a transverse electromagnetic field. And I will show a clear relationship between local-maxima and the convergence speed when calculating it with the binary spin. More precisely, the annealing path with the smallest local-maxima converges fast, even though it consumes fewer computational resources. Therefore, it is possible to induce an optimal adiabatic phase transition by selecting NSA parameters appropriately. This paper shows an effective method to choose the parameters when simulating QMC on a classical computer.
