Optimal control of two-level quantum systems
Optimal control of two-level quantum systems
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DOI：
10.1109/9.928587
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发表时间：
2001-06-01
影响因子：
6.8
通讯作者：
Dahleh, M
中科院分区：
文献类型：
--
作者：
D'Alessandro, D;Dahleh, M
本文研究了二能级量子系统的操纵。本研究的动机是量子力学逻辑门的设计，执行规定的逻辑操作的两个级别的量子系统，量子比特，我们考虑的问题，驱动的演化算子到一个期望的状态，同时最小化的能量型成本。在数学上，这个问题转化为一个最优控制问题的系统变化的李群的特殊酉矩阵的二维，成本是二次的控制。我们发展了二能级量子系统最优控制的综合理论。这包括，特别是，正常和异常极值的分类和最优控制函数的规律性的证明。本文的结果对核磁共振实验和量子计算的影响进行了讨论。
In this paper, we study the manipulation of two-level quantum systems. This research is motivated by the design of quantum mechanical logic gates which perform prescribed logic operations on a two-level quantum system, a quantum bit, We consider the problem of driving the evolution operator to a desired state, while minimizing an energy-type cost. Mathematically, this problem translates into an optimal control problem for systems varying on the Lie group of special unitary matrices of dimension two, with cost that is quadratic in the control. We develop a Comprehensive theory of optimal control for two-level quantum systems. This includes, in particular, a classification of normal and abnormal extremals and a proof of regularity of the optimal control functions. The impact of the results of the paper on nuclear magnetic resonance experiments and quantum computation is discussed.