Mathematical Theory of Generalized Duality Quantum Computers Acting on Vector-States
Mathematical Theory of Generalized Duality Quantum Computers Acting on Vector-States
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DOI：
10.1007/s10773-012-1225-4
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发表时间：
2013-06
影响因子：
1.4
通讯作者：
H. Cao;G. Long;Zhihua Guo;Zheng-Li Chen
中科院分区：
文献类型：
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作者：
H. Cao;G. Long;Zhihua Guo;Zheng-Li Chen
遵循对偶量子计算的思想，将作用于矢量态的广义对偶量子计算机定义为由广义量子分波器（GQWD）、有限个么正算符和广义量子合波器（GQWC）组成的元组。证明了GDQC的GQWD和GQWC分别是等距的和余等距的，并且是相互对偶的。证明了每个GDQC都有一个压缩，称为广义对偶量子门（GDQG）。对GDQCs进行了分类，并讨论了GDQG的性质。一些应用程序，包括两个正交的对偶量子计算机算法的无序数据库搜索和理解的马赫-曾德尔干涉仪。
Following the idea of duality quantum computation, a generalized duality quantum computer (GDQC) acting on vector-states is defined as a tuple consisting of a generalized quantum wave divider (GQWD) and a finite number of unitary operators as well as a generalized quantum wave combiner (GQWC). It is proved that the GQWD and GQWC of a GDQC are an isometry and a co-isometry, respectively, and mutually dual. It is also proved that every GDQC gives a contraction, called a generalized duality quantum gate (GDQG). A classification of GDQCs is given and the properties of GDQGs are discussed. Some applications are obtained, including two orthogonal duality quantum computer algorithms for unsorted database search and an understanding of the Mach-Zehnder interferometer.