Code Properties of the Holographic Sierpinski Triangle
Ning Bao, Joydeep Naskar
TL;DR
This paper investigates the holographic quantum error correction capabilities of Sierpinski Triangle-shaped boundary regions in AdS/CFT, revealing advantages over topological codes and limitations in higher dimensions.
Contribution
It demonstrates that Sierpinski Triangle regions in AdS_4/CFT_3 support holographic error correction, unlike in AdS_5/CFT_4, highlighting geometric influences on quantum error correction.
Findings
Sierpinski Triangle in AdS_4/CFT_3 supports holographic error correction.
Fractal boundary regions in higher dimensions may lack these properties.
Holographic codes have advantages over topological codes in certain fractal geometries.
Abstract
We study the holographic quantum error correcting code properties of a Sierpinski Triangle-shaped boundary subregion in . 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 does not possess these holographic quantum error correction properties.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Coding theory and cryptography · Advanced Data Storage Technologies