Manipulation of Eigenstates—Based on Lyapunov Method
Shuang Cong · 2014
The five chapters from Chapter 4 through Chapter 8 introduce quantum control theory based on the Lyapunov method. Chapters 4 to 6 cover the Lyapunov methods which are used in state transfer between diverse quantum states: the manipulation of eigenstates, population control, and general state control. Chapter 4 introduces the principle of the Lyapunov stability theorem and gives the control law design processes of eigenstate transfer for the Lyapunov function selected based on the state distance. We also present an optimal quantum control based on the Lyapunov stability theorem and the realization of the quantum Hadamard gate based on the Lyapunov method. Several numerical simulations and comparison results analyses are given in this chapter.