## 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

- Coherent-state constellation code
- Holographic code — The RG cat code encoder has coarse-graining features reminiscent of holography [1].

## Cousin

- Approximate quantum error-correcting code (AQECC) — RG cat codes approximately protect against displacements that represent ultraviolet coherent operators.

## 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”, (2024) arXiv:2401.17795

## 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