Double-semion code[1]

Description

Stub.

Parents

  • Modular-qudit stabilizer code — Double-semion code can be realized as a modular-qudit stabilizer code with \(q=4\) [2].
  • Abelian topological code — When treated as ground states of the code Hamiltonian, the code states realize double-semion topological order, a topological phase of matter that also exists in twisted \(\mathbb{Z}_2\) gauge theory [3].

Cousin

  • Kitaev surface code — There is a logical basis for the toric and double-semion codes where each codeword is a superposition of states corresponding to all noncontractible loops of a particular homotopy type. The superposition is equal for the toric code, whereas some loops appear with a \(-1\) coefficient for the double semion.

Zoo code information

Internal code ID: double_semion

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: double_semion

Cite as:
“Double-semion code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/double_semion
BibTeX:
@incollection{eczoo_double_semion, title={Double-semion code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/double_semion} }
Permanent link:
https://errorcorrectionzoo.org/c/double_semion

References

[1]
M. A. Levin and X.-G. Wen, “String-net condensation: A physical mechanism for topological phases”, Physical Review B 71, (2005). DOI; cond-mat/0404617
[2]
Tyler D. Ellison et al., “Pauli stabilizer models of twisted quantum doubles”. 2112.11394
[3]
R. Dijkgraaf and E. Witten, “Topological gauge theories and group cohomology”, Communications in Mathematical Physics 129, 393 (1990). DOI

Cite as:

“Double-semion code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/double_semion

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/double_semion.yml.