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].
Member of code lists
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
- Victor V. Albert (2025-06-13) — most recent
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.