Spectral analysis of the Koopman operator recovers Hamiltonian parameters in open quantum systems

Abstract: An accurate identification of Hamiltonian parameters is essential for modeling and control of open quantum systems. In this work, a novel data-driven method for inferring such parameters from first-moment dynamics is presented using an open 2D quantum harmonic oscillator as an example. The method relies on the discrete spectrum of the Koopman operator to obtain such parameters, which is obtained using the multichannel Hankel Alternative View of Koopman (mHAVOK) algorithm; a theoretical connection of such affirmation is presented. The method is tested on the expected value of noiseless quadratures, retrieving oscillation frequencies, damping rates, nonlinear Kerr shifts, qubit-photon coupling strengths of a Jaynes-Cummings interaction, and a modulated frequency of a time-dependent Hamiltonian. The majority of the recovered parameters remained within 5% of their true values. When compared to 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.