The ability to control quantum systems using shaped fields as well as to infer the states of such controlled systems from measurement data are key tasks in the design and operation of quantum devices. Here we associate the success of performing both tasks to the structure of the underlying control landscape. We relate the ability to control and reconstruct the full state of the system to the absence of singular controls, and show that for sufficiently long evolution times singular controls rarely occur. Based on these findings, we describe a learning algorithm for finding optimal controls that makes use of measurement data obtained from partially accessing the system. Open challenges stemming from the concentration of measure phenomenon in high dimensional systems are discussed.

中文翻译：

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汇总控制景观和断层扫描原理

使用成形场控制量子系统以及从测量数据推断此类受控系统状态的能力是量子器件设计和操作中的关键任务。在这里，我们将完成这两项任务的成功与底层控制格局的结构联系起来。我们将控制和重构系统完整状态的能力与不存在奇异控件联系起来，并表明对于足够长的演化时间，很少会出现奇异控件。基于这些发现，我们描述了一种学习算法，用于寻找最佳控制，该控制利用了部分访问系统后获得的测量数据。讨论了由高维系统中的测量现象集中引起的开放挑战。