\(\mathbb{Z}_3\times\mathbb{Z}_9\)-fusion subsystem code[1]
Description
Modular-qudit 2D subsystem stabilizer code whose low-energy excitations realize a non-modular anyon theory with \(\mathbb{Z}_3\times\mathbb{Z}_9\) fusion rules. Encodes two qutrits when put on a torus.Cousin
- Abelian quantum-double stabilizer code— The \(\mathbb{Z}_3\times\mathbb{Z}_9\)-fusion subsystem code can be obtained from a stack of \(q=3\) and \(q=9\) square-lattice qudit surface codes by gauging out the anyons \(m_1^{-1}e_2^3\) and \(m_2^{-1}\) [1; Sec. 7.5].
Primary Hierarchy
Parents
The \(\mathbb{Z}_3\times\mathbb{Z}_9\)-fusion subsystem code is characterized by a non-modular anyon theory with \(\mathbb{Z}_3\times\mathbb{Z}_9\) fusion rules.
\(\mathbb{Z}_3\times\mathbb{Z}_9\)-fusion subsystem code
References
- [1]
- T. D. Ellison, Y.-A. Chen, A. Dua, W. Shirley, N. Tantivasadakarn, and D. J. Williamson, “Pauli topological subsystem codes from Abelian anyon theories”, Quantum 7, 1137 (2023) arXiv:2211.03798 DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Nathanan Tantivasadakarn (2023-04-08)
- Victor V. Albert (2023-04-08)
- Victor V. Albert (2021-12-29)
Cite as:
“\(\mathbb{Z}_3\times\mathbb{Z}_9\)-fusion subsystem code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/zthree_znine, arXiv:2606.11484