Remarks on Clifford codes

Clifford codes are quantum error control codes that generalize stabilizer codes. These codes were introduced in 1996 by Knill, but only a single nonstabilizer Clifford code was known to date. We derive a necessary and sufficient condition that allows one to decide when a Clifford code is a stabilizer code. We compile a table of all true Clifford codes for error groups of small order

[1]  Y. Edel,et al.  Quantum twisted codes , 2000 .

[2]  Alexei E. Ashikhmin,et al.  Nonbinary quantum stabilizer codes , 2001, IEEE Trans. Inf. Theory.

[3]  R. Matsumoto,et al.  Constructing Quantum Error-Correcting Codes for pm-State System from Classical Error-Correcting Codes , 1999, quant-ph/9911011.

[4]  N. Sloane,et al.  Quantum error correction via codes over GF(4) , 1996, Proceedings of IEEE International Symposium on Information Theory.

[5]  Gottesman Class of quantum error-correcting codes saturating the quantum Hamming bound. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[6]  E. Knill Group representations, error bases and quantum codes , 1996, quant-ph/9608049.

[7]  John J. Cannon,et al.  The Magma Algebra System I: The User Language , 1997, J. Symb. Comput..

[8]  D. DiVincenzo,et al.  Quantum Error-Correcting Codes , 1998 .

[9]  Peter Májek,et al.  Quantum Error Correcting Codes , 2005 .

[10]  Andreas Klappenecker,et al.  Beyond stabilizer codes I: Nice error bases , 2002, IEEE Trans. Inf. Theory.

[11]  Andreas Klappenecker,et al.  Beyond stabilizer codes II: Clifford codes , 2002, IEEE Trans. Inf. Theory.

[12]  Clifford Codes , 2022 .