论文标题
非富度量子的蓬蒂古宁最佳控制
Pontryagin-Optimal Control of a non-Hermitian Qubit
论文作者
论文摘要
非热门有效的哈密顿人描述的开放系统量子动力学已成为引起兴趣的主题。对非武术物理学的研究揭示了一般原则，包括复杂特征值空间的拓扑与绝热控制策略的分解之间的关系。我们在这里研究了单个非热量子的控制，类似于最近实现的实验系统，其中非热性是由开放的自发发射通道产生的。我们回顾了由此产生的非热汉尔顿族人的拓扑特征，然后提出两个明显的结果。首先，我们说明了如何在量子量的动力学中实现任何连续和可区分的纯状轨迹，该量子的条件是不发射的。该结果隐含地为在此类非热门系统中击穿标准绝热后果的方法提供了解决方法。其次，我们使用Pontryagin的最大原理来得出连接Bloch球上边界状态的最佳轨迹，使用成本函数，该成本函数平衡所需的动力学与用于实现它们的控制器能量。我们证明，即使在检测效率低下的情况下，后一种方法也可以有效地找到保持高状态纯度的轨迹。
Open-system quantum dynamics described by non-Hermitian effective Hamiltonians have become a subject of considerable interest. Studies of non-Hermitian physics have revealed general principles, including relationships between the topology of the complex eigenvalue space and the breakdown of adiabatic control strategies. We study here the control of a single non-Hermitian qubit, similar to recently realized experimental systems in which the non-Hermiticity arises from an open spontaneous emission channel. We review the topological features of the resulting non-Hermitian Hamiltonian and then present two distinct results. First, we illustrate how to realize any continuous and differentiable pure-state trajectory in the dynamics of a qubit that are conditioned on no emission. This result implicitly provides a workaround for the breakdown of standard adiabatic following in such non-Hermitian systems. Second, we use Pontryagin's maximum principle to derive optimal trajectories connecting boundary states on the Bloch sphere, using a cost function which balances the desired dynamics against the controller energy used to realize them. We demonstrate that the latter approach can effectively find trajectories which maintain high state purity even in the case of inefficient detection.
