# On the Wilsonian meaning of quantum error correction

## TL;DR

This paper proposes a novel approach to defining renormalization group transformations using quantum error correction codes, linking RG flow, error matrices, and holographic duality concepts.

## Contribution

It introduces a method to connect RG transformations with quantum error correction, including an error beta function and its implications for holographic codes.

## Key findings

- RG transformations determined by error matrices
- Error beta function conjectured to be zero for holographic codes
- Relation between error sum rule and bulk locality discussed

## Abstract

We sketch a recipe to define renormalization group transformations based on Kadanoff-Wilson block packing using a quantum error correction code. In such a case the RG transformations of the couplings are determined by the error matrix of the QEC code. In order to define the RG transformation of couplings we use Weinberg's sum rule for an error Kallen Lehmann function. We define an error beta function that for holographic AdS codes is conjectured to be zero. For holographic codes the relation between Weinberg's sum rule for the error Kallen Lehmann function and bulk locality is briefly discussed.