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Indian Control Conference

Adaptive Observer-Based State and Parameter Estimation for Two-Level Quantum Systems Using Dynamic Regressor Extension and Mixing

Eram Taslima, Shyam Kamal, Ram Khelawan Saket

Published Dec 18, 2025• 1 citation
Publisher

Abstract

This paper presents an adaptive observer-based framework for the simultaneous state and parameter estimation of a closed two-level quantum system governed by the Liouville–von Neumann equation. The system, driven by an external laser field with unknown atom-field coupling strength, is reformulated in the Bloch sphere representation, wherein the nonlinear dynamics of the spin variables are described. To estimate the unmeasured internal states and the unknown coupling parameter, we propose a cascaded strategy combining a nonlinear adaptive observer with the Dynamic Regressor Extension and Mixing (DREM) technique. The observer reconstructs the full Bloch vector from partial measurement (population difference), and the resulting regressors enable a scalar DREM formulation for the unknown parameter. Unlike traditional gradient-based identification, the DREM-based update ensures improved noise robustness and accelerated convergence even for scalar parameters. Numerical simulations confirm the accuracy and robustness of the proposed estimation strategy, demonstrating effective reconstruction of both the quantum state and the Hamiltonian parameter under realistic noisy measurements.

DOI
10.1109/icc69100.2025.11372417

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