[Jump to code hierarchy]

Cage-net code[13]

Alternative names: String-membrane-net code.

Description

A non-stabilizer commuting-projector code obtained by coupling layers of \(G\)-graded string-net models [3]. Originally introduced independently, cage-net and string-membrane-net models are equivalent under local unitary circuits [2]. The cage-net construction can be used to realize various fracton phases, stabilizer and otherwise.

Cousins

  • Fracton stabilizer code— The cage-net construction can be used to realize various fracton phases, stabilizer and otherwise.
  • String-net code— The cage-net code is a non-stabilizer commuting-projector code obtained by coupling layers of \(G\)-graded string-net models [3].

Primary Hierarchy

Parents
Cage-net codewords form ground-state subspaces of frustration-free commuting projector Hamiltonians.
Cage-net codewords form ground-state subspaces of frustration-free commuting projector Hamiltonians.
Cage-net code
Children
A field-theoretic description of the qudit X-cube model can be obtained by coupling layers of 2D \(\mathbb{Z}_q\) gauge theory [3].

References

[1]
A. Prem, S.-J. Huang, H. Song, and M. Hermele, “Cage-Net Fracton Models”, Physical Review X 9, (2019) arXiv:1806.04687 DOI
[2]
K. Slagle, D. Aasen, and D. Williamson, “Foliated field theory and string-membrane-net condensation picture of fracton order”, SciPost Physics 6, (2019) arXiv:1812.01613 DOI
[3]
P. Gorantla, A. Prem, N. Tantivasadakarn, and D. J. Williamson, “String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to \(p\)-String Condensation”, (2025) arXiv:2505.13604
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: cage_net

Cite as:
“Cage-net code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/cage_net
BibTeX:
@incollection{eczoo_cage_net, title={Cage-net code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/cage_net} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/cage_net

Cite as:

“Cage-net code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/cage_net

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