一种构造量子稳定子码的新方法

A Novel Construction of Quantum Stabilizer Codes

量子编码是纠正或防止量子错误的有效手段,是量子计算和量子通信实用化的基础。利用循环差集(cyclic difference set)的特性,提出了一种具有循环特性的量子稳定子构造方法。通过该方法能构造出著名的[5,1,3]量子码的量子校验矩阵。通过实例分析,如[5,1]、[13,7]量子码,发现通过该方法构造的稳定子码,不仅可以编任何长度的逻辑量子信息,而且编码后的量子长度具有量子Hamming界的最小值,除此之外,该量子码具有高的码率。

Quantum error correcting code is an efficient tool to correct and prevent quantum error. It is the basic for quantum computation and quantum communications. Taking advantage of the cyclic difference set,we present a novel approach to construct quantum stabilizer codes in this paper. It＇ s not difficult to construct the well-known [ 5,1,3 ] quantum code by our approach. By analyzing the property of the quantum code constructed by this method, such as [ 5,1 ], as well as [ 13,7 ], we find all the constructed codes are the quantum Single-bound codes, and we can use this method to encode different length information. Besides, the code rate is high.