Learning dynamical systems: an example from open quantum system dynamics

TL;DR

This paper demonstrates how Koopman operator learning can effectively model and analyze the dynamics of open quantum systems, including predicting evolution, observables, and inferring symmetries from data.

Contribution

It applies Koopman operator learning to open quantum system dynamics, showing its ability to predict evolution, observables, and identify symmetries directly from data.

Findings

Successfully learned the evolution of the density matrix.

Predicted physical observables using the learned Koopman operator.

Inferred symmetries of the quantum system from spectral analysis.

Abstract

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.