Qudit X-cube model code[1]
Description
Generalization of the X-cube model code to modular qudits.Cousin
- Modular-qudit surface code— A field-theoretic description of the qudit X-cube model can be obtained by coupling layers of 2D \(\mathbb{Z}_q\) gauge theory [2].
Primary Hierarchy
Parents
A field-theoretic description of the qudit X-cube model can be obtained by coupling layers of 2D \(\mathbb{Z}_q\) gauge theory [2]. For three orthogonal foliations with \(\mathbb{Z}_q\) layers, the string-membrane-net model is equivalent to the \(\mathbb{Z}_q\) X-cube model [3]. String-membrane-net models are phase-equivalent to cage-net models under generalized local unitaries [2].
Qudit X-cube model code
Children
References
- [1]
- C. Lee, Y. Hu, G. Y. Cho, and H. Watanabe, “ZN generalizations of three-dimensional stabilizer codes”, Physical Review B 112, (2025) arXiv:2504.09847 DOI
- [2]
- P. Gorantla, A. Prem, N. Tantivasadakarn, and D. J. Williamson, “String membrane nets from higher-form gauging: An alternate route to p -string condensation”, Physical Review B 112, (2025) arXiv:2505.13604 DOI
- [3]
- 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
- [4]
- W. Shirley, K. Slagle, and X. Chen, “Universal entanglement signatures of foliated fracton phases”, SciPost Physics 6, (2019) arXiv:1803.10426 DOI
- [5]
- A. Dua, I. H. Kim, M. Cheng, and D. J. Williamson, “Sorting topological stabilizer models in three dimensions”, Physical Review B 100, (2019) arXiv:1908.08049 DOI
Page edit log
- Victor V. Albert (2025-04-20) — most recent
Cite as:
“Qudit X-cube model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/qudit_xcube