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Lyapunov-based Control Theory of Closed Quantum Systems

Authors:
Shuang Cong
Fangfang Meng

Keywords: ideal closed quantum systems; quantum systems in degenerate cases; implicit Lyapunov-based control method.

Abstract:
According to whether the internal Hamiltonians are strong regular and/or the control Hamiltonians are full connected, the quantum systems can be considered as ideal closed quantum systems or the quantum systems in degenerate cases. In this paper, we propose a unique formation of quantum Lyapunov-based control method, which is suitable for both ideal closed quantum systems and the systems in degenerate cases. This Lyapunov-based control method of closed quantum systems with unique formation is realized by means of introducing implicit Lyapunov functions into the control laws, which make the control system become strong regular and full connection. The proposed Lyapunov-based control theory can transfer from arbitrary initial states to arbitrary final states in the way of asymptotic stability. The paper gives the complete design procedure of control laws. At last, a numerical experiment of the state transfer between two mixed states in degenerate cases is given to demonstrate the effectiveness of the Lyapunov-based control theory proposed.

Pages: 32 to 37

Copyright: Copyright (c) IARIA, 2017

Publication date: February 19, 2017

Published in: conference

ISSN: 2308-3735

ISBN: 978-1-61208-530-2

Location: Athens, Greece

Dates: from February 19, 2017 to February 23, 2017