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.
References
- [1]
- X. Ni, O. Buerschaper, and M. Van den Nest, “A non-commuting stabilizer formalism”, Journal of Mathematical Physics 56, 052201 (2015) arXiv:1404.5327 DOI
Page edit log
- Victor V. Albert (2022-04-19) — most recent
Cite as:
“XS stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/xs_stabilizer