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系统科学与复杂性：英文版

TRAJECTORY TRACKING THEORY OF QUANTUM SYSTEMS

Cong Cong, Shuang, Liu, Jianxiu

Published Jan 1, 2014• 0 citations
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The orbit tracking problem of a free-evolutionary target system in closed quantum systems is solved by changing it into the state transferring problem with the help of unitary transformation.The control law designed by the Lyapunov stability theorem employs a carefully constructed virtual mechanical quantity P to ensure the system convergence.The virtual mechanical quantity P is chosen by two approaches according to the forms of limit set,where P = —pf is suitable for regular limit set and a new different P is constructed for irregular one.The proposed tracking control theory is demonstrated on a four-level quantum system by means of numerical simulation experiments.
State steering and tracking have attracted a lot of interests due to their wide applications. In this paper, we present two concrete examples of trajectory tracking of an open quantum system with time-dependent Lindblad operator which has an eigenstate |ψs(t)〉 with eigenvalue 0. We work out the first case analytically while numerically the second case. From both the cases, we find that, if changing the Lindblad operator is sufficiently slow, then the system can follow the trajectory of |ψs(t)〉 very well.