Question 34. Can stability analyses be performed on closed loop quantum learning algorithms
under uncertainties and disturbances in the measurements and control fields for
general classes of quantum systems and control objectives?
Such an analysis could give insight into how best to operate the laboratory experiments.
In principle, any optimization algorithm can be applied to quantum learning control.
For example, gradient descent and simulated annealing algorithms have been explored
in simulations [111], but the GA outperformed them in several test cases. However,
this subject has not received a thorough examination:
Question 35. Do there exist algorithms that converge with greater efficiency or robustness
than the genetic algorithm for certain classes of quantum mechanical learning control
problems?
In treating question 35 it is important to consider the ability to perform very large numbers
of quantum control experiments, which may overcome certain algorithmic shortcomings
found under more common conditions. This ability is almost unprecedented in
other applications of learning algorithms.
Another approach to quantum learning control is provided by the use of input → output mapping techniques [113,114]. These methods develop an effective map between
the inputs (i.e., the parameters or features defining the control laws) and the outputs (i.e.,
the expectation values of objective operators). A map from the control input space C to
the space of possible expectation values may be determined directly from the laboratory
input and output data; a series of these maps may be needed to cover a sufficiently large
portion of C. The control law that optimally satisfies the objectives can be identified from
these maps using a suitable learning algorithm. Logical next steps in the development of
these methods include answering:
Question 36. What methods can be used to extend the linear input–output learning control
techniques developed in [113,114] to generate nonlinear maps?
中括号的公式编号保留,能帮我翻译的,我之后可以再追加悬赏,谢谢
參考答案:问题34：对于一般等级的量子系统及其控制目标来说，在测量和控制领域充满无常性和失调性的情况下，稳定性分析能否应用在封闭回路的量子学习算法上？
这样的分析能够让我们洞察如何能最好地操作实验室试验。
从理论上讲，任何优化算法都可以被应用于量子学习控制。
例如，梯度下降法（梯度衰减法）和模拟退火算法已经在模拟试验[111]中得到研究，但GA在几种测试环境中的表现都优于它们。然而，这一研究主题并没有得到全面检验：
问题35：对于某些确定等级的量子机械学习控制问题而言，是否存在比遗传算法更加有效和稳定的算法？
要回答问题35，重要的是考虑进行数目非常庞大的量子控制实验的能力，这可能会克服在更普遍的条件下所发现的一些的算法缺陷。这种能力在其它学习算法的应用中几乎是空前的。
另一个量子学习控制的方法来自于一输入→输出映射图技术[113，114]的应用。这种方法可以在输入（例如，定义控制法则的参数或特征）和输出（例如，目标算子的期望值）之间生成有效的映射图。从控制的输入C空间到可能的期望值空间之间的映射图可以直接由实验室的输入和输出数据来决定；一系列这样的映射图可能需要覆盖C中相当大的一部分。最满足目标的控制法则可以通过使用恰当的学习算法，来由这些映射图确定。这些方法发展的下一个逻辑步骤包括解答以下问题：
问题36：什么方法可以用来扩展在[113，114]中开发出的线性输入—输出学习控制技术，从而生成非线性映射图？
