Learning dynamical systems: an example from open quantum system dynamics
This work provides a method for interpreting and forecasting quantum dynamics, but it is incremental as it applies an existing algorithm to a specific domain.
The paper tackled the problem of learning dynamical systems in open quantum systems by applying Koopman operator learning to a small spin chain with dephasing gates, resulting in efficient learning of the density matrix evolution and physical observables, and enabling inference of symmetries from data.
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.