Restricted allowable generalized quantum gates |
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Authors: | HuaiXin Cao Li Li ZhengLi Chen Ye Zhang ZhiHua Guo |
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Institution: | (1) Information Sciences, Tokyo University of Science, Yamazaki 2641, 278-8510 Noda, Japan;(2) Mathematical Physics, Steklov Mathematical Institute, Gubkin St 8, 119991 Moscow, Russia; |
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Abstract: | An allowable generalized quantum gate (introduced by Long, Liu and Wang) has the form of U = Σ
k=0
d−1
c
k
U
k
, where U
k’s are unitary operators on a Hilbert space H and |Σ
k=0
d−1
c
k
|⩽1 and |c
k
|⩽1 (0⩽k⩽d−1). In this work we consider a kind of AGQGs, called restricted allowable generalized quantum gates (RAGQGs), satisfying
0 < Σ
k=0
d−1|c
k
|⩽1. 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). |
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Keywords: | duality computer Hilbert space unitary quantum gate restricted allowable generalized quantum gate |
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