Code Properties of the Holographic Sierpinski Triangle

Abstract

We study the holographic quantum error correcting code properties of a Sierpinski Triangle-shaped boundary subregion in $Ad{S}_4/CF{T}_3$. Due to existing no-go theorems in topological quantum error correction regarding fractal noise, this gives holographic codes a specific advantage over topological codes. We then further argue that a boundary subregion in the shape of the Sierpinski gasket in $Ad{S}_5/CF{T}_4$ does not possess these holographic quantum error correction properties.

Errors corrected. Journal version

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Cited by in corpus (4)

• Tensor networks for quantum computing
• Reconstruction wedges in $AdS/CFT$ with boundary fractallike structures
• Revisiting holographic codes with fractal-like boundary erasures
• Exploring uberholography