Three-fermion (3F) model code[1]
Description
A 3D topological code whose low-energy excitations realize the three-fermion anyon theory [2–4] and that can be used as a resource state for fault-tolerant MBQC [1].
Gates
Clifford gates can be performed by braiding and fusing symmetry defects in the MBQC model.
Fault Tolerance
Fault-tolerant MBQC protocol by encoding in, braiding, and fusing symmetry defects.
Parents
- Qubit stabilizer code
- Walker-Wang model code — The Walker-Wang model code reduces to the 3F model code when the input category \(\mathcal{C}=3F\) [1].
- Abelian topological code — When treated as ground states of the code Hamiltonian, 3F model code states realize 3F topological order, which is chiral and modular.
Cousin
- Three-fermion (3F) subsystem code — The 3F model cluster-like state encodes the temporal gate operations on the 3F subsystem code into a third spatial dimension [1]. In addition, one of possible 2D boundaries of the 3F model code is effectively a 2D 3F subsystem code.
References
- [1]
- S. Roberts and D. J. Williamson, “3-Fermion topological quantum computation”, (2020) arXiv:2011.04693
- [2]
- E. Rowell, R. Stong, and Z. Wang, “On classification of modular tensor categories”, (2009) arXiv:0712.1377
- [3]
- H. Bombin, M. Kargarian, and M. A. Martin-Delgado, “Interacting anyonic fermions in a two-body color code model”, Physical Review B 80, (2009) arXiv:0811.0911 DOI
- [4]
- H. Bombin, G. Duclos-Cianci, and D. Poulin, “Universal topological phase of two-dimensional stabilizer codes”, New Journal of Physics 14, 073048 (2012) arXiv:1103.4606 DOI
Page edit log
- Victor V. Albert (2023-03-28) — most recent
Cite as:
“Three-fermion (3F) model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/three_fermion