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：机器学习算法旨在从数据中学习动态系统，可用于预测、控制和解释观察到的动态。在这项工作中，我们以开放量子系统动力学为例，说明了Koopman算子学习算法的使用。我们将研究与淬灭门耦合的小自旋链的动力学，并展示Koopman算子学习是一种有效学习密度矩阵演化及与系统相关的所有物理可观测量的方法。最后，通过利用所学Koopman算子的谱分解，我们展示了可以直接从数据中推断出潜在动态所遵循的对称性。