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Hopf-algebra cluster-state code[1,2]

Description

Code based on a cluster state defined on qudits valued in a Hopf algebra. This code has also been extended to weak Hopf algebras [2].

Cousins

  • Hopf-algebra quantum-double code— Both Hopf-algebra quantum-double and Hopf-algebra cluster-state codes are defined on qudits valued in a Hopf algebra.
  • Group-based cluster-state code— Hopf-algebra cluster-state codes reduce to group-based cluster-state codes for finite groups when the Hopf algebra reduces to a finite group.

Member of code lists

Primary Hierarchy

Quantum Domain
Category Kingdom
Category-based quantum codeQECC Quantum
Parents
Category-based quantum code
Hopf-algebra cluster-state code
Children
Modular-qudit cluster-state code
Hopf-algebra cluster-state codes reduce to modular-qudit cluster-state codes when the Hopf algebra reduces the group \(\mathbb{Z}_q\).

References

[1]
Z. Jia, “Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation”, Journal of High Energy Physics 2024, (2024) arXiv:2405.09277 DOI
[2]
Z. Jia, “Weak Hopf non-invertible symmetry-protected topological spin liquid and lattice realization of (1+1)D symmetry topological field theory”, (2024) arXiv:2412.15336
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Zoo Code ID: hopf_cluster_state

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

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/categories/hopf/hopf_cluster_state.yml.