Contents

# 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 $\{-1\} \notin S \subset \mathcal{P}_n$ of the Pauli group $\mathcal{P}_n$ acting on a register of $n$ q-bits.

Conversely, $S \subset \mathcal{P}_n$ 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.

## References

Stabilizer codes were introduced, independeny, in

following

Review:

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