Due to the fault of the author(s) of the article entitled “Quantum quasi-cyclic low-density parity-check error-correcting codes”, published in Chinese Physics B, 2009, Vol. 18, Issue 10, pp 4154--4160, has been found to partly copy from the article arXiv:quant-ph/0701020v2 on the arXiv preprint. So the above article in Chinese Physics B has been withdrawn from the publication. [2 February 2010]
In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasi-cyclic (QC) low-density parity-check (LDPC) codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated.