On the robustness of stabilizing feedbacks for quantum spin-1/2 systems

Weichao Liang (1, 2) , Nina Amini (3) , Paolo Mason (3)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 CY - CY Cergy Paris Université
3 L2S - Laboratoire des signaux et systèmes

In this paper, we consider stochastic master equations describing the evolution of quantum spin-1/2 systems interacting with electromagnetic fields undergoing continuous-time measurements. We suppose that the initial states and the exact values of the physical parameters are unknown. We prove that the feedback stabilization strategy considered in [16] is robust to these imperfections. This is shown by studying the asymptotic behavior of the coupled stochastic master equations describing the evolutions of the actual state and the estimated one under appropriate assumptions on the feedback controller. We provide sufficient conditions on the feedback controller and a valid domain of estimated parameters which ensure exponential stabilization of the coupled system. Furthermore, our results allow us to answer positively to [15, Conjecture 4.4] in the case of spin-1/2 systems with unknown initial states, even in presence of imprecisely known physical parameters.

Domaines: Optimisation et contrôle [math.OC]

Weichao Liang, Nina Amini, Paolo Mason. On the robustness of stabilizing feedbacks for quantum spin-1/2 systems. 2020 59th IEEE Conference on Decision and Control (CDC), Dec 2020, Jeju Island, South Korea. pp.3842-3847, ⟨10.1109/cdc42340.2020.9304009⟩. ⟨hal-03015492⟩