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 stabilizer 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
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Zoo Code ID: groupoid_surface

Cite as:
“Groupoid toric code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/groupoid_surface
BibTeX:
@incollection{eczoo_groupoid_surface, title={Groupoid toric code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/groupoid_surface} }
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“Groupoid toric code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/groupoid_surface

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/categories/groupoid_surface.yml.