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].

Parent

  • Abelian topological code — The semion code is a subsystem code characterized by the chiral semion topological phase.

Cousins

References

[1]
T. D. Ellison et al., “Pauli topological subsystem codes from Abelian anyon theories”, (2022) arXiv:2211.03798
[2]
J. Haah, “Clifford quantum cellular automata: Trivial group in 2D and Witt group in 3D”, Journal of Mathematical Physics 62, 092202 (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
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Zoo Code ID: semion

Cite as:
“Chiral semion subsystem code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/semion
BibTeX:
@incollection{eczoo_semion,
  title={Chiral semion subsystem code},
  booktitle={The Error Correction Zoo},
  year={2023},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/semion}
}
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Permanent link:
https://errorcorrectionzoo.org/c/semion

Cite as:

“Chiral semion subsystem code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/semion

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qudits/subsystem/topological/semion.yml.