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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
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Zoo Code ID: generalized_color

Cite as:
“Generalized 2D color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/generalized_color
BibTeX:
@incollection{eczoo_generalized_color, title={Generalized 2D color code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/generalized_color} }
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Permanent link:
https://errorcorrectionzoo.org/c/generalized_color

Cite as:

“Generalized 2D color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/generalized_color

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/groups/topological/2d/generalized_color.yml.