Hsieh Michael, Wu Rebing, Rabitz Herschel
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
J Chem Phys. 2009 Mar 14;130(10):104109. doi: 10.1063/1.2981796.
A broad class of quantum control problems entails optimizing the expectation value of an observable operator through tailored unitary propagation of the system density matrix. Such optimization processes can be viewed as a directed search over a quantum control landscape. The attainment of the global extrema of this landscape is the goal of quantum control. Local optima will generally exist, and their enumeration is shown to scale factorially with the system's effective Hilbert space dimension. A Hessian analysis reveals that these local optima have saddlepoint topology and cannot behave as suboptimal extrema traps. The implications of the landscape topology for practical quantum control efforts are discussed, including in the context of nonideal operating conditions.
一大类量子控制问题需要通过对系统密度矩阵进行定制的幺正演化来优化可观测量算符的期望值。这种优化过程可以看作是在量子控制态势面上的有向搜索。实现该态势面的全局极值是量子控制的目标。一般会存在局部最优解，并且已表明其数量随系统的有效希尔伯特空间维数呈阶乘增长。海森矩阵分析表明，这些局部最优解具有鞍点拓扑结构，不能作为次优极值陷阱。讨论了态势面拓扑结构对实际量子控制工作的影响，包括在非理想操作条件的背景下。
