量子系统中基于李雅普诺夫稳定性理论的叠加态的制备

在量子系统中利用被控系统的本征值，构造用来进行坐标旋转的幺正矩阵．通过幺正变换操作抵消系统每个状态所具有的局部相位，并选择变换后的被控状态与目标态之间的误差作为李雅普诺夫函数．在此基础上，基于李雅普诺夫稳定性理论，在保证控制系统稳定的前提下进行控制律的设计，给出了系统状态制备所需控制的详细设计过程，并对结果进行了对比分析．最后，在一个自旋1／2粒子系统上，采用本文所提方法分别对目标态是本征态和叠加态的制备进行了系统仿真实验，并对系统状态演化时间与不同参数情况下控制值之间的关系进行了分析．

Superposition state preparation based on Lyapunov stability theorem in quantum systems

The unitary matrix was constructed by using eigenstates of the controlled quantum system so as to perform a coordinate rotation on the controlled system. In such a way the local phases of all states of the system were eliminated. Then the error between the controlled state and the target state after transformation was selected as the Lyapunov function, and the system control law was designed based on Lyapunov stability theorem with the pre-condition that the system is kept stable. The detailed design procedure of the controller needed for preparation of the system states and the comparison analysis of the results were given. Finally, the system simulation experiments on a spin-1/2 particle system were implemented to prepare both the eigen and superposition target states with the proposed control method, and the relation between the system state evolution time and control value was analyzed with different parameters.