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Study of Several Problems in Asymmetric Quantum Error-correcting Codes

Author: DengZuo
Tutor: LiLei
School: Nanjing University of Posts and Telecommunications
Course: Applied Mathematics
Keywords: Quantum error correction code Asymmetric quantum error correction code Polynomial basis Quasi- winding code Subsystem code
CLC: O413
Type: Master's thesis
Year: 2012
Downloads: 30
Quote: 0
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Abstract


In recent years , quantum computing technology because of its superior computing power and sparked a high degree of attention and in-depth research . Especially quantum error correction code technology to overcome the quantum decoherence of the quantum noise , which greatly promoted the realization of the process of the development of quantum computers and quantum communication . However , before most of the research on quantum error correction code in the symmetry of the quantum channel , the amount of so - called symmetric subchannels is the quantum bit error frequency is equal to the quantum phase frequency error occurred . This study focuses on the more realistic asymmetric quantum channel , that is , the physical implementation of the program in the quantum phase error is greater than the frequency of occurrence of the frequency of the quantum bit error occurs . In this paper, the classical theory of error-correcting codes and quantum error correcting code theory based on a study . The specific research work as follows : 1 . Classical polynomial code gives a new polynomial - based asymmetric quantum error correction code construction process is mainly based on the polynomial basis structure mapping to be met constructed Theorem necessary conditions for a class of code . 2 classic often cyclic code construct asymmetric quantum constant cyclic code , and further asymmetric quantum error correcting code is given a uniform construction method . This method proposed is based on cyclic code , often cyclic codes , quasi - cyclic codes , and quasi- winding of the close ties between the code to the constructor unified the asymmetric quantum quasi wound code constructor up . Using the subsystem code and the classical cyclic nature of the code , we construct a class based on the the asymmetric cyclic code subsystem code and gives a unified structure asymmetric subsystem code constructor . Asked the same of this method is based on cyclic code , often cyclic code , the close ties between the quasi - cyclic codes and quasi - winding code .

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