  The recent success in constructing asymptotically good quantum low-density
parity-check (QLDPC) codes makes this family of codes a promising candidate for
error-correcting schemes in quantum computing. However, conventional belief
propagation (BP) decoding of QLDPC codes does not yield satisfying performance
due to the presence of unavoidable short cycles in their Tanner graph and the
special degeneracy phenomenon. In this work, we propose to decode QLDPC codes
based on a check matrix with redundant rows, generated from linear combinations
of the rows in the original check matrix. This approach yields a significant
improvement in decoding performance with the additional advantage of very low
decoding latency. Furthermore, we propose a novel neural belief propagation
decoder based on the quaternary BP decoder of QLDPC codes which leads to
further decoding performance improvements.
