基于欧氏几何的量子CSS码的构造

Construction of Quantum CSS Codes Based on Euclidean Geometry

利用有限几何中的点和线,构造出低密度奇偶校验(LDPC)码的校验矩阵。根据这种LDPC码的特点,通过对校验矩阵的行或列变换得到其对偶码,从而获得基于CSS码的量子LDPC码。以量子码(15,4)为例,验证了这种量子LDPC码构造算法的可行性。在仅考虑比特翻转信道下对该量子码进行性能分析,结果表明用这种方法易于得到其对偶码,并且得到的量子码比经典码有更好的性能。

Based on the lines and points in finite geometry, a method to construct the low density parity check codes is discussed in this paper. According to the characteristics of these codes, the dual codes of this kind of LDPC codes are obtained by splitting the rows or columns of the check matrix. A novel construction method of quantum low-density-parity-check code is developed according to the theory of quantum CSS codes. Quantum code （ 15, 4） is selected as an example to illustrate the availability of this construction method, and its performance is analyzed under the bit-flipping channel. It is shown that this method is easier to construct the dual codes, and the performance of quantum codes constructed is superior to that of classical ones.