Groupoid toric code[1]
Description
Extension of the Kitaev surface code from abelian groups to groupoids, i.e., multi-fusion categories in which every morphism is an isomorphism [2]. Some models admit fracton-like features such as extensive ground-state degeneracy and excitations with restricted mobility. The robustness of these features has not yet been established.
Parent
- Multi-fusion string-net code — Groupoid toric-code categories are unitary multi-fusion categories based on matrix algebras [3], so groupoid toric codes can equivalently be formulated as multi-fusion string-net codes.
Cousin
- Fracton code — Some groupiod toric code models admit fracton-like features such as extensive ground-state degeneracy and excitations with restricted mobility.
References
- [1]
- P. Padmanabhan and I. Jana, “Groupoid Toric Codes”, (2022) arXiv:2212.01021
- [2]
- R. Brown, “From Groups to Groupoids: a Brief Survey”, Bulletin of the London Mathematical Society 19, 113 (1987) DOI
- [3]
- L. Chang et al., “On enriching the Levin–Wen model with symmetry”, Journal of Physics A: Mathematical and Theoretical 48, 12FT01 (2015) arXiv:1412.6589 DOI
Page edit log
- Victor V. Albert (2022-12-05) — most recent
- Meng Cheng (程蒙) (2022-12-05)
Cite as:
“Groupoid toric code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/groupoid_surface