Mathematical Theory of Generalized Duality Quantum Computers Acting on Vector-States

作者：Cao, Huai-Xin^*; Long, Gui-Lu; Guo, Zhi-Hua; Chen, Zheng-Li

来源：International Journal of Theoretical Physics, 2013, 52(6): 1751-1767.

DOI：10.1007/s10773-012-1225-4

• Generalized duality quantum computer
• Divider
• Combiner
• Generalized duality quantum gate

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.

• 出版日期2013-6
• 单位陕西师范大学