Mathematical Theory of Generalized Duality Quantum Computers Acting on Vector-States |
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Authors: | Huai-Xin Cao Gui-Lu Long Zhi-Hua Guo Zheng-Li Chen |
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Institution: | 1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China 2. Tsinghua National Laboratory for Information Science and Technology, Beijing, 100084, China
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Abstract: | 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. |
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