Generalized color code[1]

Description

Member of a family of non-Abelian topological codes, defined by a finite group \( G \), that serves as a generalization of the color code (for which \(G=\mathbb{Z}_2\)).

Parents

Cousins

  • Quantum-double code — 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 \(G\).
  • Color code — The generalized color code for \(G=\mathbb{Z}_2\) reduces to the 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 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 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 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/tree/main/codes/quantum/groups/generalized_color.yml.