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Zbl 1136.81019
Zeng, Guihua; Li, Yuan; Guo, Ying; Lee, Moon Ho
Stabilizer quantum codes over the Clifford algebra. (English)
[J] J. Phys. A, Math. Theor. 41, No. 14, Article ID 145304, 8 p. (2008). ISSN 1751-8113; ISSN 1751-8121/e

Summary: The key problem for constructing a stabilizer quantum code is how to create a set of generators for the stabilizer of the stabilizer quantum code, i.e. check matrix. In this paper, we suggest an approach based on the Clifford algebra to create the check matrix for the stabilizer quantum codes. In the proposed approach, the recursive relation of the matrix transform over the Clifford algebra is employed to generate the check matrix. With the proposed approach, a quantum code with any length can be constructed easily. Especially some new codes, which are impossible via previous approaches, are constructed.

MSC 2000:: *81P68 Quantum computation and quantum cryptography
15A66 Clifford algebras

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