nLab stabilizer code




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.


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)


Stabilizer codes were introduced, independeny, in



  • Simeon Ball, Aina Centelles, Felix Huber, Section 2 of: Quantum error-correcting codes and their geometries (arXiv:2007.05992)

See also

Realization in experiment:

Realization of quantum error correction in experiment:

Last revised on May 5, 2021 at 13:05:33. See the history of this page for a list of all contributions to it.