Spectral analysis of the Koopman operator as a framework for recovering Hamiltonian parameters in open quantum systems

Accurate identification of Hamiltonian parameters is essential for modeling and controlling open quantum systems. In this work, we demonstrate that the multichannel Hankel alternative view of the Koopman ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>m</a:mi> <a:mi>HAVOK</a:mi> </a:mrow> </a:math> ) algorithm is a robust and reliable spectral data-driven method for retrieving Hamiltonian parameters from the evolution of first-moment observables in open quantum systems. The method relies on the discrete spectrum of the Koopman operator to obtain these parameters, which are computed using the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>m</b:mi> <b:mi>HAVOK</b:mi> </b:mrow> </b:math> algorithm; a theoretical justification for this approach is presented. The method is tested on noiseless quadratures of an open two-dimensional quantum harmonic oscillator and shown to retrieve oscillation frequencies, damping rates, nonlinear Kerr shifts, the qubit-photon coupling strength of a Jaynes-Cummings interaction, and the modulated frequency of a time-dependent Hamiltonian. The majority of the recovered parameters remained within 5% of their actual values. Compared with Fourier- and matrix-pencil estimators, our approach yields lower errors for dynamics with strong dissipation. Overall, these findings suggest that Koopman operator theory provides a practical framework for studying quantum dynamical systems.