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 \(G=\mathbb{Z}_2\times\mathbb{Z}_2\)).Decoding
Chromöbius, an open-source implementation of the Möbius decoder works for many 2D color codes [2].Cousins
- Group GKP code— Generalized color-code Hamiltonians should be expressable in terms of \(X\)- and \(Z\)-type operators of group-GKP codes; see [3; Sec. 3.3].
- 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 \(G\).
- Modular-qudit color code— The generalized color code for \(G=\mathbb{Z}_q\) reduces to the 2D modular-qudit color code.
Member of code lists
Primary Hierarchy
Parents
The anyon theory corresponding to a generalized color code is a trivial-cocycle TQD associated with the group \(G \times G/[G,G]\), where \(G\) is any finite group.
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
- [2]
- C. Gidney and C. Jones, “New circuits and an open source decoder for the color code”, (2023) arXiv:2312.08813
- [3]
- V. V. Albert, D. Aasen, W. Xu, W. Ji, J. Alicea, and J. Preskill, “Spin chains, defects, and quantum wires for the quantum-double edge”, (2021) arXiv:2111.12096
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