\(U(d)\)-covariant approximate erasure code[1,2] 

Description

Covariant code whose construction takes in an arbitrary erasure-correcting code to yield an approximate QECC that is also covariant with respect to the unitary group.

Parents

Cousin

  • Five-qubit perfect code — The five-qubit code can be used to construct an approximate code that is also covariant with respect to the unitary group.

References

[1]
M. P. Woods and Á. M. Alhambra, “Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames”, Quantum 4, 245 (2020) arXiv:1902.07725 DOI
[2]
Y. Yang, Y. Mo, J. M. Renes, G. Chiribella, and M. P. Woods, “Optimal universal quantum error correction via bounded reference frames”, Physical Review Research 4, (2022) arXiv:2007.09154 DOI
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Zoo Code ID: nonabelian_covariant_erasure

Cite as:
“\(U(d)\)-covariant approximate erasure code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/nonabelian_covariant_erasure
BibTeX:
@incollection{eczoo_nonabelian_covariant_erasure, title={\(U(d)\)-covariant approximate erasure code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/nonabelian_covariant_erasure} }
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Cite as:

“\(U(d)\)-covariant approximate erasure code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/nonabelian_covariant_erasure

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/properties/block/covariant/nonabelian_covariant_erasure.yml.