Double-semion code[1]




  • 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].


  • 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

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Zoo Code ID: double_semion

Cite as:
“Double-semion code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
@incollection{eczoo_double_semion, title={Double-semion code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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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
Tyler D. Ellison et al., “Pauli stabilizer models of twisted quantum doubles”. 2112.11394
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.