On mathematical theory of the duality computers

  • Authors:

  • Xiangfu Zou;Daowen Qiu;Lihua Wu;Lvjun Li;Lvzhou Li

  • Affiliations:

  • Department of Computer Science, Zhongshan University, Guangzhou, People's Republic of China 510275 and Department of Mathematical and Physics, Wuyi University, Jiangmen, People's Republic of China ...;Department of Computer Science, Zhongshan University, Guangzhou, People's Republic of China 510275;Department of Computer Science, Zhongshan University, Guangzhou, People's Republic of China 510275;Department of Computer Science, Zhongshan University, Guangzhou, People's Republic of China 510275;Department of Computer Science, Zhongshan University, Guangzhou, People's Republic of China 510275

  • Venue:
  • Quantum Information Processing
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

Recently, Long proposed a new type of quantum computers called duality computers or duality quantum computers. The duality computers based on the general quantum interference principle are much more powerful than an ordinary quantum computer. A mathematical theory for the duality computers has been presented by Gudder. However, he pointed out that a paradoxical situation of the mathematical theory occurs between the mixed state formalism and the pure state formalism. This paper argues for Gudder's mathematical theory of the duality computers for the mixed state formalism. First, we point out two problems existing in the pure state description of the duality computers. Then, we present a new mathematical theory of the duality computers for the pure state formalism according with Gudder's mixed state description, generalize the new mathematical theory of the duality computers in the density matrix formalism, and discuss some basic properties of the divider operators and combiner operators of the duality computers. The new mathematical theory can conquer the two problems mentioned above. Finally, we find that the nonunitary operations can be performed on every path of a quantum wave divider of the duality computers. Especially, we discuss in detail that the subwaves interact with environment by a CNOT gate.