量子误差控制的傅里叶变换方法
On the Fourier Transform Approach to Quantum Error Control
摘要：
量子码是量子系统的状态空间的子空间，用于保护量子信息。一些常见的量子码类型是稳定子（或加性）码、从稳定子码获得的非稳定子（或非加性）码和克利福德码。这些分析的框架中使用傅立叶变换的有限群，有限群的问题是一个小组的量子错误组考虑。所有类别的代码，可以在这个框架中得到的探索，包括代码更一般的Clifford码。这些更一般的类（“直接和Clifford码的翻译”）的错误检测性能的特点。构造了实例代码，并给出了计算机代码搜索结果并进行了分析。
英文摘要：
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from stabilizer codes, and Clifford codes. These are analyzed in a framework using the Fourier transform on finite groups, the finite group in question being a subgroup of the quantum error group considered. All the classes of codes that can be obtained in this framework are explored, including codes more general than Clifford codes. The error detection properties of one of these more general classes ("direct sums of translates of Clifford codes") are characterized. Examples codes are constructed, and computer code search results presented and analysed.
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