**Dynamical models and feedback issues for super-conducting quantum circuits**

This lecture relies on recent physical experiments conducted on quantum super-conducting circuits. It presents the structure of the dynamical models (stochastic master equation) governing the input/output relationships for such circuits made of linear capacitors/inductors and Josephson junctions (nonlinear inductors) that are connected to transmission lines. The control input signals are associated to classical oscillatory waves, propagating along these transmission lines towards the circuit, with well defined amplitudes and frequencies in the micro-wave range. The output classical signals correspond to quantum measurements of the waves scattered back and based on homodyne/heterodyne detection schemes. This lecture will also described the two feedback strategies for stabilizing such systems: measurement-based feedback, where the controller is a classical system producing classical control signals depending on the quantum-measurement outcomes, which are also classical signals; coherent feedback (also called autonomous feedback or reservoir/dissipation engineering) where the controller is a dissipative quantum system in coherent interaction with the quantum system to be controlled.

| Prof. Pierre Rouchon Centre Automatique et Systèmes MinesParisTechFrancia |

Prof. Pierre Rouchon graduated from Ecole Polytechnique in 1983, and obtained his Ph.D. in Chemical Engineering from Mines ParisTech in 1990. In 2000 and his “Habilitation à Diriger des Recherches” in Mathematics from University Paris-Sud Orsay. From 1993 to 2005, he was associated professor at Ecole Polytechnique in Applied Mathematics. From 1998 to 2002, he was the head of the Centre Automatique et Systèmes of Mines ParisTech. He is now professor at Mines ParisTech. His fields of interest include nonlinear control and system theory with its applications. His contributions include differential flatness and its extension to infinite dimensional systems, nonlinear observers and symmetries, process control, motion planing and tracking for mechanical systems, feedback stabilization and estimation for electrical drives, internal combustion engines and quantum systems.