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  • Open Access

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

Jorge E. Pérez-García, Carlos Colchero, and Julio C. Gutiérrez-Vega*

  • *Contact author: juliocesar@tec.mx
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Phys. Rev. A 113, 042222 – Published 21 April, 2026

DOI: https://doi.org/10.1103/v5zg-gybr

Abstract

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 (mHAVOK) 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 mHAVOK 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.

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Phys. Rev. A 113, 042222– Published 21 April, 2026
  • Received 2 December 2025
  • Accepted 31 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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