探索受约束的量子控制景观
Exploring constrained quantum control landscapes
摘要：
利用外部场优化控制量子系统的广泛成功归因于底层控制景观的有利拓扑结构，其中景观是作为控制的函数的物理可观察性。控制景观可以被证明不包含次优的捕获极值后，合理的物理假设的满意度，但这种拓扑分析并不成立时，控制资源的重大限制。本工作采用模拟探索的拓扑结构和功能的控制景观的纯态人口转移与一类受约束的控制字段。的字段参数化的一组均匀间隔的频谱频率，与相关的相位作为控制。优化结果表明，确保在目标状态下的高产率所需的相位控制的最小数量具有特殊的依赖于量子系统中可访问的能级的数量，揭示了从分析的第一和第二阶变化的产量相对于控制。当采用的控制和/或弱控制通量的数量不足，捕获极值和鞍点上的景观观察。当控制资源是足够灵活的，解决方案产生的全球最大的产量被发现形成连续可变的控制领域，保持产量的连接“水平集”。这些最佳的产量水平集被发现缩小到孤立的点上的顶部的景观作为控制领域的通量减少，进一步减少的通量变成这些点次优捕获极值的景观。虽然受约束的控制字段可以有多种形式，超出了这里讨论的情况，但本文中发现的行为说明了约束可能带来的影响。
英文摘要：
The broad success of optimally controlling quantum systems with external fields has been attributed to the favorable topology of the underlying control landscape, where the landscape is the physical observable as a function of the controls. The control landscape can be shown to contain no suboptimal trapping extrema upon satisfaction of reasonable physical assumptions, but this topological analysis does not hold when significant constraints are placed on the control resources. This work employs simulations to explore the topology and features of the control landscape for pure-state population transfer with a constrained class of control fields. The fields are parameterized in terms of a set of uniformly spaced spectral frequencies, with the associated phases acting as the controls. Optimization results reveal that the minimum number of phase controls necessary to assure a high yield in the target state has a special dependence on the number of accessible energy levels in the quantum system, revealed from an analysis of the first- and second-order variation of the yield with respect to the controls. When an insufficient number of controls and/or a weak control fluence are employed, trapping extrema and saddle points are observed on the landscape. When the control resources are sufficiently flexible, solutions producing the globally maximal yield are found to form connected `level sets' of continuously variable control fields that preserve the yield. These optimal yield level sets are found to shrink to isolated points on the top of the landscape as the control field fluence is decreased, and further reduction of the fluence turns these points into suboptimal trapping extrema on the landscape. Although constrained control fields can come in many forms beyond the cases explored here, the behavior found in this paper is illustrative of the impacts that constraints can introduce.
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