Renormalization group (RG) cat code[13] 

Description

Code whose codespace is spanned by \(q\) field-theoretic coherent states which are flowing under the renormalization group (RG) flow of massive free fields. The code approximately protects against displacements that represent local (i.e., short-distance, ultraviolet, or UV) operators. Intuitively, this is because RG cat codewords represent non-local (i.e., long-distance) degrees of freedom, which should only be excitable by acting on a macroscopically large number of short-distance degrees of freedom.

Protection

Approximately protects against displacements that represent ultraviolet coherent operators, i.e., short-distance degrees of freedom of the field theory.

Parents

Cousin

References

[1]
K. Furuya, N. Lashkari, and S. Ouseph, “Real-space RG, error correction and Petz map”, Journal of High Energy Physics 2022, (2022) arXiv:2012.14001 DOI
[2]
K. Furuya, N. Lashkari, and M. Moosa, “Renormalization group and approximate error correction”, Physical Review D 106, (2022) arXiv:2112.05099 DOI
[3]
T. Kuwahara et al., “Quantum Error Correction Realized by the Renormalization Group in Scalar Field Theories”, Progress of Theoretical and Experimental Physics 2024, (2024) arXiv:2401.17795 DOI
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Zoo Code ID: rg_cat

Cite as:
“Renormalization group (RG) cat code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rg_cat
BibTeX:
@incollection{eczoo_rg_cat, title={Renormalization group (RG) cat code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/rg_cat} }
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Cite as:

“Renormalization group (RG) cat code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rg_cat

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/coherent_state/cat/rg_cat.yml.