Efficient Quantum Stabilizer Codes: LDPC and LDPC-Convolutional Constructions
Efficient Quantum Stabilizer Codes: LDPC and LDPC-Convolutional Constructions
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DOI：
10.1109/tit.2009.2034794
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发表时间：
2010
影响因子：
2.5
通讯作者：
P. Tan;Jing Li
中科院分区：
文献类型：
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作者：
P. Tan;Jing Li
现有的由经典二进制码构造的量子稳定子码完全属于Calderbank-Shor-Steane(CSS)码的特殊子类。本文提出了五种基于经典二进制准循环低密度奇偶校验(LDPC)码和经典二进制LDPC-卷积码的非码字稳定子码的系统构造，填补了这一空白。这些新的构造利用了结构化稀疏图，基本利用了包括级联、旋转和加扰在内的简单而强大的编码技术，并生成了具有广泛长度和速率的丰富的码类。我们推导了每个结构满足一般辛内积(SIP)条件的充分条件，并给出了这些码的实用译码算法。所得到的码是源于经典二进制码(而不是GF(4)上的码)的第一类非CS量子LDPC码和非CS量子卷积码，其中一些码的性能与现有的量子码相当或更好。
Existing quantum stabilizer codes constructed from the classic binary codes exclusively belong to the special subclass of Calderbank-Shor-Steane (CSS) codes. This paper fills in the gap by proposing five systematic constructions for non-CSS stabilizer codes, the first four of which are based on classic binary quasi-cyclic low-density parity-check (LDPC) codes and last on classic binary LDPC-convolutional codes. These new constructions exploit structured sparse graphs, make essential use of simple and powerful coding techniques including concatenation, rotation and scrambling, and generate rich classes of codes with a wide range of lengths and rates. We derive the sufficient, and in some cases also the necessary, conditions for each construction to satisfy the general symplectic inner product (SIP) condition, and develop practical decoder algorithms for these codes. The resulting codes are the first classes of non-CSS quantum LDPC codes and non-CSS quantum convolutional codes rooted from classic binary codes (rather than codes in GF(4)), and some of them perform as well as or better than the existing quantum codes.