Chiral semion subsystem code[1]
Description
Modular-qudit subsystem stabilizer code with qudit dimension \(q=4\) that is characterized by the chiral semion topological phase. Admits a set of geometrically local stabilizer generators on a torus.
Encoding
Unitary encoder applied to a 3D stack of 2D surface codes, realizing chiral semion topological order at one of its surfaces [2,3].
Parents
- Subsystem modular-qudit stabilizer code
- Lattice subsystem code
- Abelian topological code — The semion code is a subsystem code characterized by the chiral semion topological phase.
Cousins
- Double-semion stabilizer code — The semion code can be obtained from the double-semion stabilizer code by gauging out the anyon \(\bar{s}\) [1; Fig. 15].
- \(\mathbb{Z}_q^{(1)}\) subsystem code — The semion code can be obtained from the \(\mathbb{Z}_4^{(1)}\) subsystem code by condensing the anyon \(s^2\) [1; Fig. 15].
References
- [1]
- T. D. Ellison et al., “Pauli topological subsystem codes from Abelian anyon theories”, Quantum 7, 1137 (2023) arXiv:2211.03798 DOI
- [2]
- J. Haah, “Clifford quantum cellular automata: Trivial group in 2D and Witt group in 3D”, Journal of Mathematical Physics 62, (2021) arXiv:1907.02075 DOI
- [3]
- W. Shirley et al., “Three-Dimensional Quantum Cellular Automata from Chiral Semion Surface Topological Order and beyond”, PRX Quantum 3, (2022) arXiv:2202.05442 DOI
Page edit log
- Nathanan Tantivasadakarn (2023-04-08) — most recent
- Victor V. Albert (2023-04-08)
- Victor V. Albert (2021-12-29)
Cite as:
“Chiral semion subsystem code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/semion