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The natural trajectory tracking problem is studied for generic quantum states represented by density operators. A control design based on the Hilbert-Schmidt distance as a Lyapunov function is considered. The control dynamics is redefined on an extended space where the LaSalle invariance principle can be correctly applied even for non-stationary target states. LaSalle's invariance principle is used...
This paper deduces and analyzes the invariant set in quantum Lyapunov control, explores the principles for constructing and adjusting diagonal elements of a diagonal Lyapunov function, and achieves the convergence to any goal state in some invariant subset of closed loop systems by using dynamical system theory and energy-level connectivity graph. Research results show that if a goal state is an eigenstate...
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