Description
Covariant code whose construction takes an arbitrary erasure-correcting code as input and yields an approximate QECC that is also covariant with respect to the unitary group.Cousin
- \([[5,1,3]]\) 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.
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Parents
Any finite-dimensional code covariant w.r.t. a continuous group has to be approximate because of the Eastin-Knill theorem.
\(U(d)\)-covariant approximate erasure code
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
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2022-07-26)
Cite as:
“\(U(d)\)-covariant approximate erasure code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/nonabelian_covariant_erasure, arXiv:2606.11484