Algebraic geometric construction of a quantum stabilizer code

Details Algebraic geometric construction of a quantum stabilizer code Algebraic geometric construction of a quantum stabilizer code

2001-07-26

arxiv.org/abs/quant-ph/0107129v3

Physics

Quantum Physics

LaTeX2e, 12 pages, 1 color figure. A decoding method was added and several typographical errors were corrected in version 2. T

Scientific paper

10.1109/TIT.2002.1013156

The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a construction method of such a self-orthogonal space using an algebraic curve. By using the proposed method we construct an asymptotically good sequence of binary stabilizer codes. As a byproduct we improve the Ashikhmin-Litsyn-Tsfasman bound of quantum codes. The main results in this paper can be understood without knowledge of quantum mechanics.

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