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.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.
- 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 \([[n,k,d_X/d_Z,w]]\).
Primary Hierarchy
Parents
Calderbank-Shor-Steane (CSS) stabilizer code
Children
Homological rotor codes are rotor CSS codes constructed from chain complexes over the integers in an extension of the qubit CSS-to-homology correspondence to rotors. The homology group of the logical operators has a torsion component because the chain complexes are defined over the ring of integers, which yields codes with finite logical dimension. Products of chain complexes can also yield rotor codes.
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
Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/groups/stabilizer/css.yml.