Feedback stabilization of discrete-time quantum systems subject to non-demolition measurements with imperfections and delays

• Published in: Automatica (Oxford) Vol. 49; no. 9; pp. 2683 - 2692
• Main Authors: Amini, Hadis, Somaraju, Ram A., Dotsenko, Igor, Sayrin, Clément, Mirrahimi, Mazyar, Rouchon, Pierre
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.09.2013; Elsevier
• Subjects: Applied sciences; Automation; Classical and quantum physics: mechanics and fields; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control theory. Systems; Convergence; Delay; Exact sciences and technology; Feedback; Feedback stabilization; Markov chain; Markov processes; Mathematical analysis; Mathematics; Measurement-based feedback; Modelling and identification; Optimization and Control; Photon-number states (Fock states); Photons; Physics; Quantum computation; Quantum filter; Quantum information; Quantum non-demolition measurements; Quantum Physics; Quantum theory; Strict control Lyapunov function; Markov chain; Strict control Lyapunov function; Photon-number states (Fock states); Measurement-based feedback; Quantum filter; Feedback stabilization; Quantum non-demolition measurements; Markov process; State feedback; Quantum system; Fock space; Error probability; Feedback regulation; Conditional probability; Discrete time processes; Modeling; Delay; Quantum nondemolition measurement; Defect; System identification; Measurement error; Closed loop; Role playing; Almost sure convergence; Stochastic matrix; Stationary state; Finite state machine; Cavity electrodynamics; Observable; Kraus operator; Filter; Discrete time; Open loop; Output feedback; Lyapunov function; Signal to noise ratio

We consider a controlled quantum system whose finite dimensional state is governed by a discrete-time nonlinear Markov process. In open-loop, the measurements are assumed to be quantum non-demolition (QND). The eigenstates of the measured observable are thus the open-loop stationary states: they are...