Three-fermion (3F) model code[1] 

Description

A 3D topological code whose low-energy excitations realize the three-fermion anyon theory [24] 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

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
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Zoo Code ID: three_fermion

Cite as:
“Three-fermion (3F) model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/three_fermion
BibTeX:
@incollection{eczoo_three_fermion,
  title={Three-fermion (3F) model code},
  booktitle={The Error Correction Zoo},
  year={2023},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/three_fermion}
}
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Permanent link:
https://errorcorrectionzoo.org/c/three_fermion

Cite as:

“Three-fermion (3F) model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/three_fermion

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/stabilizer/topological/three_fermion.yml.