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Exponential stabilization of quantum systems subject to non-demolition measurements in continuous time

Gerardo Cardona Sanchez 1, 2
2 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, MINES ParisTech - École nationale supérieure des mines de Paris, SU - Sorbonne Université, Inria de Paris
Abstract : In this thesis, we develop control methods to stabilize quantum systems in continuous-time subject to quantum nondemolition measurements. In open-loop such quantum systems converge towards a random eigenstate of the measurement operator. The role of feedback is to prepare a prescribed eigenstate with unit probability. The novel element to achieve this is the introduction of an exogenous Brownian motion to drive the control actions. By using standard stochastic Lyapunov techniques, we show global exponential stability of the closed-loop dynamics. We explore as well the design of the control layer for a quantum error correction scheme in continuous-time. Another theme of interest is towards the implementation of efficiently computable control laws in experimental settings. In this direction, we propose the use control laws and of reduced-order filters which only track classical characteristics of the system, corresponding to the populations on the measurement eigenbasis. The formulation of these reduced filters is important to address the scalability issues of the filter posed by the advancement of quantum technologies.
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Gerardo Cardona Sanchez. Exponential stabilization of quantum systems subject to non-demolition measurements in continuous time. Automatic Control Engineering. Université Paris sciences et lettres, 2019. English. ⟨NNT : 2019PSLEM032⟩. ⟨tel-02378226⟩

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