Machine learning algorithms designed to learn dynamical systems from data can be used to forecast, control and interpret the observed dynamics. In this work we exemplify the use of one of such algorithms, namely Koopman operator learning, in the context of open quantum system dynamics. We will study the dynamics of a small spin chain coupled with dephasing gates and show how Koopman operator learning is an approach to efficiently learn not only the evolution of the density matrix, but also of every physical observable associated to the system. Finally, leveraging the spectral decomposition of the learned Koopman operator, we show how symmetries obeyed by the underlying dynamics can be inferred directly from data.

翻译：旨在从数据中学习动力系统的机器学习算法可用于预测、控制和解释观测到的动力学行为。本文以开放量子系统动力学为背景，展示了其中一种算法——即库普曼算子学习——的应用实例。我们将研究一个与退相位门耦合的小型自旋链的动力学，并说明库普曼算子学习如何有效地不仅学习密度矩阵的演化，还能学习与系统相关的每个物理可观测量的演化。最后，利用所学库普曼算子的谱分解，我们展示了如何直接从数据中推断出潜在动力学所遵循的对称性。