Abstract

This work considers an open two-level quantum system evolving under coherent and incoherent piecewise constant controls constrained in their magnitude and variations. The control goal is to steer an initial pure density matrix into a given target density matrix in a minimal time. A machine learning algorithm was developed, which combines the approach of \(k\) nearest neighbors and training a multi-layer perceptron neural network, to predict suboptimal final times and controls. For 18 sets of initial pure states with different size (between 10 and 200) training datasets were constructed. The numerical results are described, including the analysis of the dependence of the quality of the machine learning algorithm on the size of the training set.

中文翻译：

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机器学习，用于寻找开放式两级量子系统的次优最终时间以及相干和非相干控制

摘要

这项工作考虑了一个开放的两级量子系统，该系统在相干和不相干的分段常数控制下受其大小和变化的约束而演化。控制目标是在最短的时间内将初始的纯密度矩阵引导到给定的目标密度矩阵中。开发了一种机器学习算法，该算法结合了\（k \）最近邻居的方法并训练了多层感知器神经网络，以预测次优的最终时间和控制。对于18套不同大小（在10到200之间）的初始纯状态，构建了训练数据集。描述了数值结果，包括分析机器学习算法的质量对训练集大小的依赖性。