XS stabilizer code[1]

Description

A type of stabilizer code where stabilizer generators are elements of the group \( \{\alpha I, X, \sqrt{Z}]\}^{\otimes n} \), with \( \sqrt{Z} = \text{diag} (1, i)\). The codespace is a joint \(+1\) eigenspace of a set of stabilizer generators, which need not commute to define a valid codespace.

Parent

  • XP stabilizer code — The XP stabilizer formalism reduces to the XS formalism at \(N=4\).

Cousin

  • Abelian topological code — Twisted quantum double models for the groups \(\mathbb{Z}_2^k\) can be realized as XS stabilizer codes.

Zoo code information

Internal code ID: xs_stabilizer

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: xs_stabilizer

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

References

[1]
X. Ni, O. Buerschaper, and M. Van den Nest, “A non-commuting stabilizer formalism”, Journal of Mathematical Physics 56, 052201 (2015). DOI; 1404.5327

Cite as:

“XS stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/xs_stabilizer

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