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Table of contents
1 Résumé
1.1 Contexte
1.2 Énoncé du problème et idée principale
1.3 Plan de la thèse
2 Introduction
2.1 Background
2.2 Problem statement and main idea
2.3 Thesis outline
3 Quantum non-demolition measurements and feedback
3.1 QND measurements
3.2 Control problem and existing feedback designs
3.2.1 Static output feedback
3.2.2 State feedback
3.3 Main contribution: noise-assisted feedback stabilization .
4 Exponential stabilization of a qubit
4.1 Introduction
4.2 Qubit system
4.3 Static output feedback on a qubit
4.4 Noise assisted stabilization of Qubit eigenstates
4.5 Reduced order filtering on the qubit
4.6 Moving beyond a qubit: generation of GHZ states
4.7 Conclusions
5 Exponential stabilization of a QND eigenstate
5.1 Introduction
5.2 Connectivity graph and Laplacian matrix
5.3 Exponential stabilization via noise-assisted feedback
5.4 Approximated quantum filtering
5.5 Simulations
5.6 Conclusions
6 On continuous-time quantum error correction
6.1 Introduction
6.2 Dynamics of the three-qubit bit-flip code
6.3 Some open issues on continuous-time QEC
6.4 Error correction as noise-assisted feedback stabilization .
6.4.1 Controller design
6.4.2 Closed-loop exponential stabilization
6.4.3 Reduced order filtering
6.4.4 On the protection of quantum information
6.5 Conclusions
7 Concluding remarks and perspectives
7.1 Towards robust control methods for quantum information processing
7.2 Towards dynamical output feedback controllers
A Lyapunov’s second method for stochastic stability
A.1 Lyapunov functions for QND systems
