Abstract
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.
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