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.Member of code lists
Primary Hierarchy
Parents
The RG cat code encoder has coarse-graining features reminiscent of holography [1].
RG cat codes approximately protect against displacements that represent ultraviolet coherent operators.
Renormalization group (RG) cat code
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, R. Nasu, G. Tanaka, and A. Tsuchiya, “Quantum Error Correction Realized by the Renormalization Group in Scalar Field Theories”, Progress of Theoretical and Experimental Physics 2024, (2024) arXiv:2401.17795 DOI
Page edit log
- Victor V. Albert (2022-12-29) — most recent
Cite as:
“Renormalization group (RG) cat code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rg_cat