Copyright © 2010 Ying Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We demonstrate how to fast construct quantum error-correction codes based on quadratic residues Pauli block transforms. The present quantum codes have an advantage of being fast designed from Abelian groups on the basis of Pauli block matrices that can be yielded from quadratic residues with much efficiency.