# 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].

## Parents

- Qubit stabilizer code
- Abelian quantum-double stabilizer code — Matching codes were inspired by the \(\mathbb{Z}_2\) topological order phase of the Kitaev honeycomb model [3].

## Child

## Cousin

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

## 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

## Page edit log

- Victor V. Albert (2021-12-29) — most recent

## Cite as:

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