Dynamical Mode Decomposition for Infinite-Dimensional Open Quantum Systems; Liouvillian Spectral Analysis and Parameter Estimation

Dynamic mode decomposition (DMD) is a data-driven method for the estimation, prediction, and control of complex dynamical systems, which has gained much attention in the fields of nonlinear dynamics and fluid mechanics. A DMD method for quantum spin systems, described by a linear dynamical system of a finite-dimensional set of observables, has been proposed recently. In this study, we propose two DMD methods applicable to infinite-dimensional open quantum systems, which use time-series data obtained by quantum state tomography. First, we propose a kernel DMD method for a data-driven spectral analysis of the Liouville superoperator. Second, we propose a method for the parameter estimation of the Liouville superoperator, which incorporates prior knowledge of the model structure into DMD. The proposed methods can accurately reconstruct the system dynamics and show that DMD frameworks can be applicable to infinite-dimensional open quantum systems.