Reliable Quantum LDPC Codes over GF(4)
Yixuan Xie, Jinhong Yuan · 2016
We propose a method of constructing quantum LDPC codes from multiplicative groups of order p - 1, where p = 4n + 1 is a prime for some positive integer n. The proposed quantum LDPC codes of non-CSS structure are constructed from a pair of classical regular quasi-cyclic (QC) LDPC codes. We show that these classical regular QC-LDPC codes without cycles of length 4 are orthogonal with respect to the symplectic inner product. Moreover, the proposed construction method yields a large number of new quantum LDPC codes with various code lengths and rates. The performance of the proposed quantum LDPC codes over quantum depolarizing channels with an iterative belief-propagation decoding algorithm is evaluated by simulations.