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arXiv:1201.1387 · Automatica

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

Nina H. Amini, Ram Somaraju, I. Dotsenko, C. Sayrin, Mazyar Mirrahimi, Pierre Rouchon

Published Jul 22, 2013• 51 citations
arXivHTMLPDF
DOI
10.1016/j.automatica.2013.06.012

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A feedback scheme, stabilizing an arbitrary photon-number state in a microwave cavity, is analyzed. The quantum non-demolition measurement of the cavity state allows in open-loop a non-deterministic preparation of photon-number states. By the mean of a controlled classical field injection, this preparation process is made deterministic. The system evolves through a discrete-time Markov process and the feedback law relies on Lyapunov techniques. This feedback design compensates an unavoidable pure delay by a stochastic version of a Kalman-type predictor. After illustrating the efficiency of the proposed feedback law through simulations, the global closed-loop convergence is proved. It relies on tools from stochastic stability analysis. A brief study of the Lyapunov exponents of the linearized system around the target state gives a strong indication of the robustness of the method.