Generalized 2D color code[1]
Description
Member of a family of non-Abelian 2D topological codes, defined by a finite group \( G \), that serves as a generalization of the color code (for which \(G=\mathbb{Z}_2\times\mathbb{Z}_2\)). Hamiltonians are stabilized by group-based right- and left-multiplication \(X\)-type as well as \(Z\)-type error operators.Cousin
- Modular-qudit color code— The generalized color code for \(G=\mathbb{Z}_q\) reduces to the 2D modular-qudit color code.
Primary Hierarchy
Parents
A generalized color code for group \(G\) on the 4.8.8 lattice is equivalent to a \(G\) quantum double model and another \(G/[G,G]\) quantum double model defined using the Abelianization of \(G\).
Generalized 2D color code
Children
The generalized color code for \(G=\mathbb{Z}_2\) reduces to the 2D color code.
References
- [1]
- C. G. Brell, “Generalized color codes supporting non-Abelian anyons”, Physical Review A 91, (2015) arXiv:1408.6238 DOI
Page edit log
- Victor V. Albert (2022-12-31) — most recent
Cite as:
“Generalized 2D color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/generalized_color