## Description

A stabilizer code admitting a set of stabilizer generators that are either \(Z\)-type or \(X\)-type operators. The two sets of stabilizer generators can often, but not always, be related to parts of a chain complex over the appropriate ring or field.

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## Cousins

- Group GKP code — Group GKP codes are stabilized by \(X\)-type group-based error operators representing \(H\) and all \(Z\)-type operators that are constant on \(K\). However, the \(Z\)-type operators are not unitary for non-Abelian groups.
- Rotor stabilizer code — A rotor stabilizer code admitting a set of generators such that each generator consists of either angular position or angular momentum operators is a CSS code.
- Quantum lattice code — Quantum lattice codes defined on rectangular lattices are CSS codes. There is no known relation to chain complexes for such codes. More general lattices, obtained from rectangular lattices by Gaussian transformations, yield non-CSS codes.
- Bosonic stabilizer code — An oscillator stabilizer code admitting a set of generators such that each generator consists of either position or momentum operators is a CSS code.
- Asymmetric quantum code — In the context of comparing weight as well as of determining distances for noise models biased toward \(X\)- or \(Z\)-type errors, an extended notation for asymmetric CSS block quantum codes is \([[n,k,(d_X,d_Z),w]]\) or \([[n,k,d_X/d_Z,w]]\).

## Page edit log

- Victor V. Albert (2023-04-11) — most recent

## Cite as:

“Calderbank-Shor-Steane (CSS) stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/css