Cartan decomposition of a two-qutrit gate  

作　　者：DI YaoMin ZHANG Jie WEI HaiRui 

机构地区：[1]School of Physics&Electronic Engineering,Xuzhou Normal University,Xuzhou 221116,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2008年第11期1668-1676,共9页中国科学：物理学、力学、天文学（英文版）

基　　金：the National Natural Science Foundation of China (Grant No. 60433050);the Key Project of the Science Foundation of Xuzhou Normal University, China (Grant No. 06XLA05)

摘　　要：The decomposition of matrices corresponding to the 2-qutrit logic gate by succes-sive Cartan decomposition is investigated, and written in an exponential form based on the relationship between Lie group and Lie algebra, thus making them able to relate with the control field and the Hamiltonian of the system to perform the gate. Finally the decomposition of the ternary SWAP gate is presented in detail.The decomposition of matrices corresponding to the 2-qutrit logic gate by successive Cartan decomposition is investigated, and written in an exponential form based on the relationship between Lie group and Lie algebra, thus making them able to relate with the control field and the Hamiltonian of the system to perform the gate. Finally the decomposition of the ternary SWAP gate is presented in detail.

关 键 词：CARTAN decomposition CARTAN SUBALGEBRA 2-qutrit system TERNARY SWAP GATE 

分 类 号：O152.5[理学—数学]