dorsal/arxiv
View SchemaA Family of Quantum Stabilizer Codes Based on the Weyl Commutation Relations over a Finite Field
| Authors | V. Arvind, K. R. Parthasarathy |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0206174 |
| URL | https://arxiv.org/abs/quant-ph/0206174 |
Abstract
Using the Weyl commutation relations over a finite field we introduce a family of error-correcting quantum stabilizer codes based on a class of symmetric matrices over the finite field satisfying certain natural conditions. When the field is GF(2) the existence of a rich class of such symmetric matrices is demonstrated by a simple probabilistic argument depending on the Chernoff bound for i.i.d symmetric Bernoulli trials. If, in addition, these symmetric matrices are assumed to be circulant it is possible to obtain concrete examples by a computer program. The quantum codes thus obtained admit elegant encoding circuits.
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"abstract": "Using the Weyl commutation relations over a finite field we introduce a\nfamily of error-correcting quantum stabilizer codes based on a class of\nsymmetric matrices over the finite field satisfying certain natural conditions.\nWhen the field is GF(2) the existence of a rich class of such symmetric\nmatrices is demonstrated by a simple probabilistic argument depending on the\nChernoff bound for i.i.d symmetric Bernoulli trials. If, in addition, these\nsymmetric matrices are assumed to be circulant it is possible to obtain\nconcrete examples by a computer program. The quantum codes thus obtained admit\nelegant encoding circuits.",
"arxiv_id": "quant-ph/0206174",
"authors": [
"V. Arvind",
"K. R. Parthasarathy"
],
"categories": [
"quant-ph"
],
"title": "A Family of Quantum Stabilizer Codes Based on the Weyl Commutation Relations over a Finite Field",
"url": "https://arxiv.org/abs/quant-ph/0206174"
},
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