Title :
Comparison of unitary evolution operator decompositions in quantum systems
Author :
Cong, Shuang ; Dong, Ning
Author_Institution :
Dept. of Autom., Univ. of Sci. & Technol. of China, Hefei, China
Abstract :
The purpose of controlling a quantum system is to steer the system from an initial state to a target state. Such a control problem can be changed into the problem of generating the desired unitary evolution operators by using an appropriate decomposition. By means of the desired state´s exponential factor product theorem in the right-invariant system, the desired unitary evolution operators of a quantum system can be obtained. This paper investigates the functions and features of the Magnus decomposition, the Wei-Norman decomposition, the Lie Group decomposition and the Cartan decomposition contrastively and respectively. Properties and realization performance of those decompositions are analyzed, too. Each type of decomposition applied to different situations is also given.
Keywords :
Lie groups; quantum computing; Cartan decomposition; Lie Group decomposition; Magnus decomposition; Wei-Norman decomposition; exponential factor product theorem; quantum system control; right-invariant system; unitary evolution operator decompositions; Differential equations; Equations; Matrix decomposition; Quantum mechanics; Trajectory; quantum system; the Cartan decomposition; the Lie Group decomposition; the Magnus decomposition; the Wei-Norman decomposition;
Conference_Titel :
Control and Decision Conference (CCDC), 2011 Chinese
Conference_Location :
Mianyang
Print_ISBN :
978-1-4244-8737-0
DOI :
10.1109/CCDC.2011.5968218
