基于李雅普诺夫量子系统控制方法的状态调控

从多方面对基于李雅普诺夫的量子系统控制方法进行了系统深入地研究, 包括该方法与最优控制的关系; 李雅普诺夫函数与性能指标之间的关系; 几种常用李雅普诺夫函数下的控制所能解决的问题, 适用范围和所存在的问题等. 在此基础上, 结合量子系统本身所具有的特点, 分别针对本征态, 叠加态和混合态的制备与调控目标, 总结出多种不同控制问题的改进方案. 对不同改进方案的设计思想, 所能解决的问题, 物理意义及其适用范围等进行剖析, 系统化了一套基于李雅普诺夫稳定性理论对量子系统进行状态调控的设计方法.

State manipulation in Lyapunov-based quantum system control methods

We investigate in depth the Lyapunov-based quantum control methods including the relation between the Lyapunov-based control and the optimal control, the Lyapunov function and the performance index, the range of application and the existing problems. Combining our results with intrinsic properties of quantum system, we develop several control schemes with improvements for different objectives such as the regulation of eigenstates, superposition state or mixed state. The design ideas, the physical significance and the range of suitable applications are analyzed. The designs method employing Lyapunov stability theorem in controlling quantum system is systemized.