量子李雅普诺夫控制方法综述。
A survey of quantum Lyapunov control methods.
作者信息
Cong Shuang, Meng Fangfang
机构信息
Department of Automation, University of Science and Technology of China, Hefei 230027, China.
出版信息
ScientificWorldJournal. 2013 May 27;2013:967529. doi: 10.1155/2013/967529. Print 2013.
The condition of a quantum Lyapunov-based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two situations are classified: nondegenerate cases and degenerate cases. For these two situations, respectively, in this paper the target state is divided into four categories: the eigenstate, the mixed state which commutes with the internal Hamiltonian, the superposition state, and the mixed state which does not commute with the internal Hamiltonian. For these four categories, the quantum Lyapunov control methods for the closed quantum systems are summarized and analyzed. Particularly, the convergence of the control system to the different target states is reviewed, and how to make the convergence conditions be satisfied is summarized and analyzed.
一种可很好地应用于封闭量子系统的基于量子李雅普诺夫的控制条件是，该方法能使系统收敛而非仅仅稳定。在量子李雅普诺夫控制的收敛性研究中，分为两种情况：非简并情形和简并情形。针对这两种情况，本文分别将目标态分为四类：本征态、与内部哈密顿量对易的混合态、叠加态以及与内部哈密顿量不对易的混合态。针对这四类，总结并分析了封闭量子系统的量子李雅普诺夫控制方法。特别地，回顾了控制系统到不同目标态的收敛性，并总结和分析了如何满足收敛条件。
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