Nonstabilizer Quantum Codes from Abelian Subgroups of the Error Group

Details Nonstabilizer Quantum Codes from Abelian Subgroups of the Error Group Nonstabilizer Quantum Codes from Abelian Subgroups of the Error Group

2002-10-12

arxiv.org/abs/quant-ph/0210097v1

Physics

Quantum Physics

29 pages, latex file with 6 figures as pstex and pstex_t files

Scientific paper

This paper is motivated by the computer-generated nonadditive ((5,6,2)) code described in an article by Rains, Hardin, Shor and Sloane. We describe a theory of non-stabilizer codes of which the nonadditive code of Rains et al is an example. Furthermore, we give a general strategy of constructing good nonstabilizer codes from good stabilizer codes and give some explicit constructions and asymptotically good nonstabilizer codes. In fact, we explicitly construct a family of distance 2 non-stabilizer codes over all finite fields of which the ((5,6,2)) is an special example. More interestingly, using our theory, we are also able to explicitly construct examples of non-stablizer quantum codes of distance 3. Like in the case of stabilizer codes, we can design fairly efficient encoding and decoding procedures.

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