求解量子控制问题的一种直接离散方法  

A Direct Discretization Method of Solving Quantum Control Problems

作　　者：梅自艳 王汉权[1] MEI Zi-yan;WANG Han-quan(School of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming 650221,China;School of Mathematics,Yunnan Normal University,kunming,650504,China)

机构地区：[1]云南财经大学统计与数学学院,云南昆明650221 [2]云南大学滇池学院,云南昆明650504

出　　处：《云南民族大学学报（自然科学版）》2024年第1期133-140,共8页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(11871418,11971120);云南省自然科学基金(202101AS070044);云南大学滇池学院基础教学部科学研究项目(2023DYJC04).

摘　　要：量子控制论作为一门新兴的交叉学科,有许多内容需要研究.如何把激发态解最优地操控至基态解的量子控制问题模型就是一个待解决的问题.本篇论文针对此问题提出一种直接离散方法:先用有限差分法对量子控制问题进行直接离散,使之变为一个普通的约束优化问题,继而借助普通优化问题的求解方法得到原问题的解,最后结合MATLAB编程.数值试验结果验证了这一直接方法在求解量子控制问题上的高效性.Quantum control,as a new interdisciplinary subject,has many points to be studied.The quantum control problem model of how to optimally manipulate the excited state solution to the ground state solution is a problem to be solved.In this paper,we propose a direct discretization method for this problem:Firstly,the quantum control problem is directly discretized by the finite difference method,which makes it be an ordinary constrained optimization problem.Then,the solution of the original problem is obtained by solving the ordinary optimization problem.Finally,combined with MATLAB programming.The numerical results show that this direct method is efficient in solving quantum control problems.

关 键 词：量子控制 有限差分 离散 优化 

分 类 号：O244[理学—计算数学]