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.


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
T. D. Ellison et al., “Pauli Stabilizer Models of Twisted Quantum Doubles”, PRX Quantum 3, (2022). DOI; 2112.11394
R. Dijkgraaf and E. Witten, “Topological gauge theories and group cohomology”, Communications in Mathematical Physics 129, 393 (1990). DOI
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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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“Double-semion code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.