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理论物理通讯：英文版

Quantum BCH Codes Based on Spectral Techniques

Guo Guo, Ying Ying, Zeng, Guihua Guihua

Published Jan 1, 2006• 1 citation
OpenAlex

Abstract

当在量信号处理的时间变量是分离的时， Fouriertransform 在 Galois 域 F_2 上在 n 元组的向量空间存在，它在量信号的调查起一个重要作用。由使用 Fourier 变换，编码理论的量的想法能在与看见那不同的一个背景被描述那远。QuantumBCH 代码能被定义为状态有其量的代码某些指定连续光谱到零的部件平等者和改正错误的能力被数字也描述连续零。而且，译码量代码能与更多的效率幽灵似地被描述。

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当在量信号处理的时间变量是分离的时， Fouriertransform 在 Galois 域 F_2 上在 n 元组的向量空间存在，它在量信号的调查起一个重要作用。由使用 Fourier 变换，编码理论的量的想法能在与看见那不同的一个背景被描述那远。QuantumBCH 代码能被定义为状态有其量的代码某些指定连续光谱到零的部件平等者和改正错误的能力被数字也描述连续零。而且，译码量代码能与更多的效率幽灵似地被描述。
When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n -tuples over the Galois field F 2 , which plays an important role in the investigation of quantum signals. By using Fourier transforms, the idea of quantum coding theory can be described in a setting that is much different from that seen that far. Quantum BCH codes can be defined as codes whose quantum states have certain specified consecutive spectral components equal to zero and the error-correcting ability is also described by the number of the consecutive zeros. Moreover, the decoding of quantum codes can be described spectrally with more efficiency.
A quantum Bose–Chadhuri–Hocquenghem (BCH) code is constructed over Fnpm in the spectrum domain by employing Fourier transform. The constructed code may be employed to describe the characters of the quantum code over Fnp in the time domain. Each quantum state of the proposed code has certain specified consecutive spectral components equalling zeros, and the error-correcting ability of the code can hence be determined by the number of consecutive zeros in its parity spectrums. Moreover, the decoding process may be performed more efficiently by using the spectrum techniques rather than by using the traditional methods.