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Matching code[1]

Description

Member of a class of qubit stabilizer codes based on the Abelian phase of the Kitaev honeycomb model.

Realizations

Braiding of defects has been demonstrated for a five-qubit version of code [2].

Cousin

  • Kitaev honeycomb code— Matching codes were inspired by the \(\mathbb{Z}_2\) topological order phase of the Kitaev honeycomb model [3].

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Parents
Qubit stabilizer code
Abelian quantum-double stabilizer codeLattice stabilizer QLDPC Stabilizer Abelian topological Topological Hamiltonian-based QECC Quantum
Matching codes were inspired by the \(\mathbb{Z}_2\) topological order phase of the Kitaev honeycomb model [3].
Matching code
Children
XYZ\(^2\) hexagonal stabilizer code

References

[1]
J. R. Wootton, “A family of stabilizer codes for \(D({{\mathbb{Z}}_{2}})\) anyons and Majorana modes”, Journal of Physics A: Mathematical and Theoretical 48, 215302 (2015) arXiv:1501.07779 DOI
[2]
J. R. Wootton, “Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment”, Quantum Science and Technology 2, 015006 (2017) arXiv:1609.07774 DOI
[3]
A. Kitaev, “Anyons in an exactly solved model and beyond”, Annals of Physics 321, 2 (2006) arXiv:cond-mat/0506438 DOI
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Zoo Code ID: matching

Cite as:
“Matching code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/matching
BibTeX:
@incollection{eczoo_matching, title={Matching code}, booktitle={The Error Correction Zoo}, year={2021}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/matching} }
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Permanent link:
https://errorcorrectionzoo.org/c/matching

Cite as:

“Matching code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/matching

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