  In this paper, we consider quantum error correction over depolarizing
channels with non-binary low-density parity-check codes defined over Galois
field of size $2^p$ . The proposed quantum error correcting codes are based on
the binary quasi-cyclic CSS (Calderbank, Shor and Steane) codes. The resulting
quantum codes outperform the best known quantum codes and surpass the
performance limit of the bounded distance decoder. By increasing the size of
the underlying Galois field, i.e., $2^p$, the error floors are considerably
improved.
