Code whose codewords realize a 2D topological order rendered by a Chern-Simons topological field theory. The corresponding anyon theory is defined by a finite group \(G\) and a Type-III group cocycle.
A code Hamiltonian can be obtained from a 2D model with symmetry-protected topological (SPT) order by gauging the model's symmetry. The same group and cocycle data classifies both 2D SPTs and TQDs .
- Generalized 2D color code — 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.
- Quantum-double code — The anyon theory corresponding to a quantum-double code is a TQD with trivial cocycle.
- Abelian TQD stabilizer code — The anyon theory corresponding to (Abelian) TQD codes is defined by an (Abelian) group and a Type III cocycle.
- Y. Hu, Y. Wan, and Y.-S. Wu, “Twisted quantum double model of topological phases in two dimensions”, Physical Review B 87, (2013) arXiv:1211.3695 DOI
- J. Kaidi et al., “Higher central charges and topological boundaries in 2+1-dimensional TQFTs”, SciPost Physics 13, (2022) arXiv:2107.13091 DOI
- X. Chen et al., “Symmetry protected topological orders in interacting bosonic systems”, (2013) arXiv:1301.0861
Page edit log
- Victor V. Albert (2023-04-06) — most recent
“Twisted quantum double (TQD) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/tqd