Allowable Generalized Quantum Gates

HuaiXin Cao, Li Li, ZhengLi Chen +2 more

Cao, HuaiXin, LI . +6 more

Chun Li

Ye Zhang, Huaixin Cao, Li Li

Cao Huai

An allowable generalized quantum gate(introduced by Long,Liu and Wang)has the form of U 1 0 d kk k c U -= ∑,where Uk's are unitary operators on a Hilbert space H and 1 0 1 d kkc -= |∑|≤and 1 k |c|≤(0≤k≤d-1).In this work we consider a kind of AGQGs,called restricted allowable generalized quantum gates(RAGQGs),satisfying 1 0 0 1 d kk c -= ∑||≤.Some properties of the set RAGQG(H)of all RAGQGs on H are established.Especially,we prove that the extreme points of RAGQG(H)are exactly unitary operators on H and that B(H)=R+RAGQG(H).

Zhaoqi Wu, Shifang Zhang, Chuanxi Zhu

In this paper, we give a characterization of generalized quantum gates.We also show that many important operators are generalized quantumgates, moreover, some of these operators can be represented as theconvex combination of only two unitary operators. Our results answerwhat kinds of operations a duality quantum computing admits. Wepoint out that the set of all generalized quantum gates coincides withthe set of all restricted allowable generalized quantum gates. Thus,our results are also valid for restricted allowable generalized quantumgates