Qudit X-cube model code

Qudit X-cube model code[1]

Generalization of the X-cube model code to modular qudits.

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].

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].

Qudit X-cube model code

Children

The qudit X-cube model code reduces to the X-cube model code for \(q=2\). The X-cube model is a foliated type-I fracton code [3,4].

[1]: C. Lee, Y. Hu, G. Y. Cho, and H. Watanabe, “\(\mathbb{Z}_N\) generalizations of three-dimensional stabilizer codes”, (2025) arXiv:2504.09847
[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”, (2025) arXiv:2505.13604
[3]: W. Shirley, K. Slagle, and X. Chen, “Universal entanglement signatures of foliated fracton phases”, SciPost Physics 6, (2019) arXiv:1803.10426 DOI
[4]: 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

“Qudit X-cube model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/qudit_xcube