Abstract
We study the holographic quantum error correcting code properties of a Sierpinski triangle-shaped boundary subregion in ${\mathrm{AdS}}_{4}/{\mathrm{CFT}}_{3}$. 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 ${\mathrm{AdS}}_{5}/{\mathrm{CFT}}_{4}$ does not possess these holographic quantum error correction properties.
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