\(\mathbb{Z}_4^{(1)}\) subsystem code[1]
Description
Modular-qudit \(q=4\) subsystem stabilizer code realizing abelian \(\mathbb{Z}_4^{(1)}\) topological order [2]. Its anyonic exchange statistics resemble those of the double semion code, but its fusion rules realize the \(\mathbb{Z}_4\) group.
Parents
- Subsystem modular-qudit stabilizer code
- Abelian topological code — When treated as ground states of the code Hamiltonian, the code states realize \(\mathbb{Z}_4^{(1)}\) topological order [2].
- Modular-qudit surface code — The \(\mathbb{Z}_4^{(1)}\) subsystem code can be obtained from the \(\mathbb{Z}_4\) surface code by gauging out the anyon \(e m^3\) [1; Fig. 15].
References
- [1]
- T. D. Ellison et al., “Pauli topological subsystem codes from Abelian anyon theories”, (2022) arXiv:2211.03798
- [2]
- P. H. Bonderson, Non-Abelian Anyons and Interferometry, California Institute of Technology, 2007 DOI
Page edit log
- Victor V. Albert (2023-02-07) — most recent
Cite as:
“\(\mathbb{Z}_4^{(1)}\) subsystem code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qudit_z4one