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

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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.