Group-based cluster-state code[1] 

Description

Code consisting of group-based cluster states based on a finite group \(G\) [1]. Such cluster states can be defined using a graph and conditional group multiplication operations.

Parent

Child

  • Cluster-state code — Group-based cluster-state codes reduce to cluster-state codes for \(G=\mathbb{Z}_2\).

Cousins

  • Modular-qudit CWS code — A single group-based cluster-state codeword for \(G=\mathbb{Z}_q\) is used to construct a modular-qudit CWS code.
  • Galois-qudit CWS code — A group-based cluster-state codeword for \(G=GF(q)\) is used to construct a modular-qudit CWS code.

References

[1]
C. G. Brell, “Generalized cluster states based on finite groups”, New Journal of Physics 17, 023029 (2015) arXiv:1408.6237 DOI
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Zoo Code ID: group_cluster_state

Cite as:
“Group-based cluster-state code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/group_cluster_state
BibTeX:
@incollection{eczoo_group_cluster_state, title={Group-based cluster-state code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/group_cluster_state} }
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Cite as:

“Group-based cluster-state code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/group_cluster_state

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/groups/group_gkp/group_cluster_state.yml.