Algebraic geometric construction of a quantum stabilizer code
<|reference_start|>Algebraic geometric construction of a quantum stabilizer code: 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.<|reference_end|>
@article{matsumoto2001algebraic,
    title={Algebraic geometric construction of a quantum stabilizer code},
    author={Ryutaroh Matsumoto},
    journal={arXiv preprint arXiv:quant-ph/0107129},
    year={2001},
    doi={10.1109/TIT.2002.1013156},
    archivePrefix={arXiv},
    eprint={quant-ph/0107129},
    primaryClass={quant-ph cs.IT math.AG math.IT math.SG}
}