Algebraic geometric construction of a quantum stabilizer code

Abstract

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.