处理组合优化这一类 NP 问题的时候，可以采用经典的模拟退火算法，基于温度的扰 动使得系统在不同状态之间变换，寻求最优解。而在量子退火中，量子扰动扮演着相同的 角色，把量子扰动带入退火过程，目的是想让其更加快速地收敛到最优的状态。在伊辛模 型中加入横场，是一种简单的获得量子扰动的方法，从而可以将量子退火方法运用到横场 伊辛模型中。更多的，旅行商问题通过转化后能够用伊辛模型进行表示，所以就可以用基 于横场伊辛模型的量子退火的方式来进行处理。通过模拟，比较与分析计算结果，说明了 不同退火参数对退火结果的影响，也证实了在搜寻伊辛模型基态的表现上，量子退火比传 统的模拟退火更好。 本文主要分为五个部分：第一部分，阐述退火算法的相关背景以及发展；第二部分， 介绍模拟退火以及量子退火的基本原理；第三部分，详细描述退火算法在伊辛模型上的具 体计算过程，并分析计算结果；第四部分，展示退火算法在旅行商问题的运用；第五部 分，为对本文的总结与对未来的展望。

When dealing with the NP problem of combinatorial optimization, we can use the classical simulated annealing algorithm. thermal fluctuations makes the system change between different states and seek the optimal solution. In quantum annealing, quantum fluctuation plays the same role, bringing quantum fluctuation into the annealing process in order to allow it to converge to an optimal state more quickly. Adding the transverse field to the Ising model is a simple method of obtaining quantum fluctuation, so that the quantum annealing method can be applied to the transverse field Ising model.More,the traveling salesman problem can be expressed by the Ising model after conversion,so it can be processed by quantum annealing based on the transverse field Ising model. Through the simulation, comparison and analysis of the calculation results, the influence of different annealing parameters on the annealing results is illustrated. It is also proved that the quantum annealing is better than the traditional simulated annealing in the performance of searching for the ground state of the Ising model. This paper is divided into five parts: The first part,describes the background and development of the annealing algorithm;The second part,introduces the basic principles of simulated annealing and quantum annealing; The third part, describes in detail the specific calculation process of the annealing algorithmon the Ising model and analyzes the calculation results;The fourth part,shows the application of the annealing algorithm in the traveling salesman problem; The fifth part, is a summary of this paper and a vision for the future.