We investigate the realization of 2-qutrit logic gate in a bipartite 3-level system with qusi-Ising interaction. On the basis of Caftan decomposition of matrices, the unitary matrices of 2-qutrit are factorized into p...We investigate the realization of 2-qutrit logic gate in a bipartite 3-level system with qusi-Ising interaction. On the basis of Caftan decomposition of matrices, the unitary matrices of 2-qutrit are factorized into products of a series of realizable matrices. It is equivalent to exerting a certain control field on the system, and the control goal is usually gained by a sequence of control pulses. The general discussion on the realization of 2-qutrit logic gate is made first, and then the realization of the ternary SWAP gate and the ternary √SWAP gate are discussed specifically, and the sequences of control pulses and drift processes implementing these gates are given.展开更多
设L=S(m;n)是定义在特征p>3的代数闭合域F上的阶化特殊型李代数,利用已研究L的不可约表示的方法,通过定义L的如下阶化:限制情形定义L=(?)L_([q],I),非限制情形定义L=(?)L_([q],I),这里L是L的本原p-包络,有表达式L=L (?) sum from i=1...设L=S(m;n)是定义在特征p>3的代数闭合域F上的阶化特殊型李代数,利用已研究L的不可约表示的方法,通过定义L的如下阶化:限制情形定义L=(?)L_([q],I),非限制情形定义L=(?)L_([q],I),这里L是L的本原p-包络,有表达式L=L (?) sum from i=1 to m sum from (d_i=1)to (n_i-1) FD_i^(P^(d_i)),而I是{1、2,…,m}的子集,得到当p-特征标χ是正则半单时,在限制李代数情形所有不可约L_χ(L)-模都是从不可约U_χ(L_([0],I))-模诱导的;在非限制的情形,所有不可约U_(?)(U_(p^s)(L,χ))-模都是从不可约U_(?)(L_([0],I))-模诱导的,这里(?)是χ到L~*上的平凡扩张.展开更多
基金supported by the National Natural Science Foundation of China under Grant No. 60433050the Science Foundation of Xuzhou Normal University under Grant No. 06XLA05
文摘We investigate the realization of 2-qutrit logic gate in a bipartite 3-level system with qusi-Ising interaction. On the basis of Caftan decomposition of matrices, the unitary matrices of 2-qutrit are factorized into products of a series of realizable matrices. It is equivalent to exerting a certain control field on the system, and the control goal is usually gained by a sequence of control pulses. The general discussion on the realization of 2-qutrit logic gate is made first, and then the realization of the ternary SWAP gate and the ternary √SWAP gate are discussed specifically, and the sequences of control pulses and drift processes implementing these gates are given.
文摘设L=S(m;n)是定义在特征p>3的代数闭合域F上的阶化特殊型李代数,利用已研究L的不可约表示的方法,通过定义L的如下阶化:限制情形定义L=(?)L_([q],I),非限制情形定义L=(?)L_([q],I),这里L是L的本原p-包络,有表达式L=L (?) sum from i=1 to m sum from (d_i=1)to (n_i-1) FD_i^(P^(d_i)),而I是{1、2,…,m}的子集,得到当p-特征标χ是正则半单时,在限制李代数情形所有不可约L_χ(L)-模都是从不可约U_χ(L_([0],I))-模诱导的;在非限制的情形,所有不可约U_(?)(U_(p^s)(L,χ))-模都是从不可约U_(?)(L_([0],I))-模诱导的,这里(?)是χ到L~*上的平凡扩张.
