Code properties of the holographic Sierpinski triangle

Ning Bao (Computational Science Initiative, Brookhaven National Laboratory, Upton, New York 11973, USA) ; Joydeep Naskar (Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA)

We study the holographic quantum error correcting code properties of a Sierpinski triangle-shaped boundary subregion in AdS4/CFT3. 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 AdS5/CFT4 does not possess these holographic quantum error correction properties.

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      "source": "APS", 
      "value": "We study the holographic quantum error correcting code properties of a Sierpinski triangle-shaped boundary subregion in <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>/</mo><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mrow></math>. 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 <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>/</mo><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></mrow></math> does not possess these holographic quantum error correction properties."
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Published on:
14 December 2022
Publisher:
APS
Published in:
Physical Review D , Volume 106 (2022)
Issue 12
DOI:
https://doi.org/10.1103/PhysRevD.106.126006
arXiv:
2203.01379
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

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