Observer-based Hamiltonian identification for quantum systems

A symmetry-preserving observer-based parameter identification algorithm for quantum systems is proposed. Starting with a 2-level quantum system (qubit), where the unknown parameters consist of the atom-laser frequency detuning and coupling constant, we prove an exponential convergence result. The analysis is inspired by Lyapunov and adaptive control techniques and is based on averaging theory. The observer is then extended to the multi-level case where all the atom-laser coupling constants are unknown. The extension of the convergence analysis is discussed through some heuristic arguments. The relevance and the robustness with respect to various noises are tested through numerical simulations.