论文标题
时间 - 最佳量子控制和奇异协议的最优性的一般表述
A general formulation of time-optimal quantum control and optimality of singular protocols
论文作者
论文摘要
我们提出了一个普遍的理论框架，用于在哈密顿量受任意约束时找到量子系统的时间优势的统一演变。量子Brachistochrone（QB）是基于各种原理的框架，其缺点是它仅处理平等约束。尽管在某些情况下，不平等约束可以简化为平等的限制，但在某些情况下，尤其是在哈密顿量中存在漂移场时。我们无法控制的漂移出现在各种系统中。我们首先根据Pontryagin的最大原则（MP）制定框架，以处理不平等约束。新框架包含QB作为一种特殊情况，并给出了其详细的信件。其次，使用此框架，我们讨论了漂移，单数控制和不平等约束之间的一般关系。奇异控制是那些在确定最佳协议时造成麻烦的人。第三，为了克服这个问题，我们通过应用广义Legendre-Clebsch条件来得出一个奇异协议的额外必要条件。这种情况尤其揭示了单数控制的物理含义。最后，我们演示了我们的框架和结果如何在一些示例中起作用。
We present a general theoretical framework for finding the time-optimal unitary evolution of the quantum systems when the Hamiltonian is subject to arbitrary constraints. Quantum brachistochrone (QB) is such a framework based on the variational principle, whose drawback is that it deals with equality constraints only. While inequality constraints can be reduced to equality ones in some situations, there are situations where they cannot, especially when a drift field is present in the Hamiltonian. The drift which we cannot control appears in a wide range of systems. We first develop a framework based on Pontryagin's maximum principle (MP) in order to deal with inequality constraints as well. The new framework contains QB as a special case, and their detailed correspondence is given. Second, using this framework, we discuss general relations among the drift, the singular controls, and the inequality constraints. The singular controls are those that satisfy MP trivially so as to cause a trouble in determining the optimal protocol. Third, to overcome this issue, we derive an additional necessary condition for a singular protocol to be optimal by applying the generalized Legendre-Clebsch condition. This condition in particular reveals the physical meaning of singular controls. Finally, we demonstrate how our framework and results work in some examples.
