dorsal/arxiv
View SchemaNonstabilizer Quantum Codes from Abelian Subgroups of the Error Group
| Authors | V. Arvind, Piyush P Kurur, K. R. Parthasarathy |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210097 |
| URL | https://arxiv.org/abs/quant-ph/0210097 |
Abstract
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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"abstract": "This paper is motivated by the computer-generated nonadditive ((5,6,2)) code\ndescribed in an article by Rains, Hardin, Shor and Sloane. We describe a theory\nof non-stabilizer codes of which the nonadditive code of Rains et al is an\nexample. Furthermore, we give a general strategy of constructing good\nnonstabilizer codes from good stabilizer codes and give some explicit\nconstructions and asymptotically good nonstabilizer codes. In fact, we\nexplicitly construct a family of distance 2 non-stabilizer codes over all\nfinite fields of which the ((5,6,2)) is an special example. More interestingly,\nusing our theory, we are also able to explicitly construct examples of\nnon-stablizer quantum codes of distance 3. Like in the case of stabilizer\ncodes, we can design fairly efficient encoding and decoding procedures.",
"arxiv_id": "quant-ph/0210097",
"authors": [
"V. Arvind",
"Piyush P Kurur",
"K. R. Parthasarathy"
],
"categories": [
"quant-ph"
],
"title": "Nonstabilizer Quantum Codes from Abelian Subgroups of the Error Group",
"url": "https://arxiv.org/abs/quant-ph/0210097"
},
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"execution_id": "ae97c9e0-74fc-45d9-9c00-cf322b29e499",
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