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.
{ "_oai": { "updated": "2023-01-07T00:32:58Z", "id": "oai:repo.scoap3.org:74497", "sets": [ "PRD" ] }, "authors": [ { "raw_name": "Ning Bao", "affiliations": [ { "country": "USA", "value": "Computational Science Initiative, Brookhaven National Laboratory, Upton, New York 11973, USA" } ], "surname": "Bao", "given_names": "Ning", "full_name": "Bao, Ning" }, { "raw_name": "Joydeep Naskar", "affiliations": [ { "country": "USA", "value": "Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA" } ], "surname": "Naskar", "given_names": "Joydeep", "full_name": "Naskar, Joydeep" } ], "titles": [ { "source": "APS", "title": "Code properties of the holographic Sierpinski triangle" } ], "dois": [ { "value": "10.1103/PhysRevD.106.126006" } ], "publication_info": [ { "journal_volume": "106", "journal_title": "Physical Review D", "material": "article", "journal_issue": "12", "year": 2022 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2023-01-07T00:30:21.055872", "source": "APS", "method": "APS", "submission_number": "6b862e5e8e2211ed93fbd61508239648" }, "page_nr": [ 6 ], "license": [ { "url": "https://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "Published by the American Physical Society", "year": "2022" } ], "control_number": "74497", "record_creation_date": "2022-12-14T16:30:04.067807", "_files": [ { "checksum": "md5:e1ffbbfbbc1e7822d8c67217b2a05c4c", "filetype": "pdf", "bucket": "bafe54c6-72a0-4b41-bd2a-3c1a08ce1610", "version_id": "13ffa400-7553-4b32-b010-174b3485dc6e", "key": "10.1103/PhysRevD.106.126006.pdf", "size": 271884 }, { "checksum": "md5:9bd85ab80aab99ac68bb9b3d240617de", "filetype": "xml", "bucket": "bafe54c6-72a0-4b41-bd2a-3c1a08ce1610", "version_id": "324dd472-8917-4db4-ad0e-ab81e7ebdf1a", "key": "10.1103/PhysRevD.106.126006.xml", "size": 99812 } ], "collections": [ { "primary": "HEP" }, { "primary": "Citeable" }, { "primary": "Published" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "quant-ph" ], "value": "2203.01379" } ], "abstracts": [ { "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." } ], "imprints": [ { "date": "2022-12-14", "publisher": "APS" } ] }