Subsystem Galois-qudit CSS code[1,2] 

Also known as Euclidean construction subsystem code.

Description

Galois-qudit subsystem stabilizer code which admits a set of gauge-group generators which consist of either all-\(Z\) or all-\(X\) Galois-qudit Pauli strings.

These codes can be constructed from classical codes via a subsystem generalization of the CSS construction or the Hermitian construction [1,3].

Parent

Child

  • Subsystem CSS code — Subsystem Galois-qudit CSS codes reduce to subsystem qubit CSS codes for \(q=2\).

Cousin

  • Galois-qudit CSS code — Subsystem Galois-qudit CSS codes reduce to (subspace) Galois-qudit CSS codes when there is no gauge subsystem.

References

[1]
S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “Subsystem Codes”, (2006) arXiv:quant-ph/0610153
[2]
S. A. Aly and A. Klappenecker, “Constructions of Subsystem Codes over Finite Fields”, (2008) arXiv:0811.1570
[3]
A. Klappenecker and P. K. Sarvepalli, “Clifford Code Constructions of Operator Quantum Error Correcting Codes”, (2006) arXiv:quant-ph/0604161
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: galois_subsystem_css

Cite as:
“Subsystem Galois-qudit CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/galois_subsystem_css
BibTeX:
@incollection{eczoo_galois_subsystem_css, title={Subsystem Galois-qudit CSS code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/galois_subsystem_css} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/galois_subsystem_css

Cite as:

“Subsystem Galois-qudit CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/galois_subsystem_css

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits_galois/subsystem/galois_subsystem_css.yml.