A general quantum system may be steered by a control of either classical or quantum nature and the latter scenario is particularly important in many quantum engineering problems including coherent feedback and reservoir engineering. In this paper, we consider a quantum system steered by a quantum controller and explore the underlying Q–Q (quantum–quantum) control landscape features for the expectation value of an arbitrary observable of the system, with the control being the engineered initial state of the quantum controller. It is shown that the Q–Q control landscape is inherently convex, and hence devoid of local suboptima. Distinct from the landscapes for quantum systems controlled by time-dependent classical fields, the controllability is not a prerequisite for the Q–Q landscape to be trap-free, and there are no saddle points that generally exist with a classical controller. However, the forms of Hamiltonian, the flexibility in choosing initial state of the controller, as well as the control duration, can influence the reachable optimal value on the landscape. Moreover, we show that the optimal solution of the Q–Q control landscape can be readily extracted from a de facto landscape observable playing the role of an effective “observer”. For illustration of the basic Q–Q landscape principles, we consider the Jaynes–Cummings model depicting a two-level atom in the presence of a cavity quantized radiation field.

中文翻译：

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用于完全量子最优控制的固有无陷阱凸面景观

一般的量子系统可以通过经典或量子性质的控制来控制，后一种情况在许多量子工程问题中尤为重要，包括相干反馈和储层工程。在本文中，我们考虑了一个由量子控制器控制的量子系统，并探索了系统任意可观测值的期望值的潜在 Q-Q（量子-量子）控制景观特征，其中控制是工程的初始状态量子控制器。结果表明，Q-Q 控制图本质上是凸的，因此没有局部次优。与由时间相关的经典场控制的量子系统的景观不同，可控性不是 Q-Q 景观无陷阱的先决条件，并且没有经典控制器通常存在的鞍点。然而，哈密顿量的形式、控制器初始状态选择的灵活性以及控制持续时间都会影响景观上的可达最优值。此外，我们表明 Q-Q 控制景观的最佳解决方案可以很容易地从扮演有效“观察者”角色的事实上的景观可观察中提取。为了说明基本的 Q-Q 景观原理，我们考虑 Jaynes-Cummings 模型，该模型描绘了存在腔量子化辐射场的两能级原子。我们表明，Q-Q 控制景观的最佳解决方案可以很容易地从扮演有效“观察者”角色的事实上的景观可观察对象中提取出来。为了说明基本的 Q-Q 景观原理，我们考虑 Jaynes-Cummings 模型，该模型描绘了存在腔量子化辐射场的两能级原子。我们表明，Q-Q 控制景观的最佳解决方案可以很容易地从扮演有效“观察者”角色的事实上的景观可观察对象中提取出来。为了说明基本的 Q-Q 景观原理，我们考虑 Jaynes-Cummings 模型，该模型描绘了存在腔量子化辐射场的两能级原子。