nLab
stabilizer code

Contents

Idea

In quantum information theory, a stabilizer code is a quantum error correcting code whose code subspace is the fixed subspace of an abelian subgroup {1}S𝒫 n\{-1\} \notin S \subset \mathcal{P}_n of the Pauli group 𝒫 n\mathcal{P}_n acting on a register of nn q-bits.

Conversely, S𝒫 nS \subset \mathcal{P}_n is then the stabilizer subgroup of the code space, whence the name of this class of codes.

Most quantum error correcting codes known are in fact stabilizer codes.

Properties

Relation to classical binary codes

Quantum stabilizer codes are closely related to classical error correcting codes, specifically to binary linear codes.

(e.g. Ball, Centelles & Huber 20, Sec. 2.3)

References

Stabilizer codes were introduced, independeny, in

following

Review:

See also

Realization in experiment:

Realization of quantum error correction in experiment: