On mathematical theory of the duality computers

On mathematical theory of the duality computers 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

On mathematical theory of the duality computers

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Publisher
Springer Journals
Copyright
Copyright © 2009 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-008-0093-6
Publisher site
See Article on Publisher Site

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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jan 23, 2009

References

  • Mathematical theory of duality quantum computers
    Gudder, S.

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