Qubit Hamiltonian identification: A symmetry-preserving observer-based approach

Silvère Bonnabel (1) , Mazyar Mirrahimi (2) , Pierre Rouchon (3)

1 Institut Montefiore - Department of Electrical Engineering and Computer Science
2 SISYPHE - SIgnals and SYstems in PHysiology & Engineering
3 CAS - Centre Automatique et Systèmes

We consider a pure two-state quantum system illuminated by two lasers. A photo-detector captures the fluorescence of the system. We build an invariant observer which yields a (local) estimation of the wave function (or density matrix) and the two key parameters (laser de-tuning and the atom- laser coupling strength) of the hamiltonian. The design exploits the symmetries of the system and can be interpreted geometrically. The convergence proof is based on averaging arguments. Simulation with noise illustrates the robustness of the obtained estimation algorithm.

Mots clés: Quantum systems; symmetries; asymptotic observers; estimation; nonlinear systems

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

Silvère Bonnabel, Mazyar Mirrahimi, Pierre Rouchon. Qubit Hamiltonian identification: A symmetry-preserving observer-based approach. 2008 IFAC World Congress, Jul 2008, Seoul, South Korea. pp.7612-7617. ⟨hal-00485740⟩