Majorana dimers and holographic quantum error-correcting codes
Holographic quantum error-correcting codes have been proposed as toy models that describe key aspects of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. In this work, we introduce a versatile framework of Majorana dimers capturing the intersection of stabilizer and Gaussian Major...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2019-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.1.033079 |
| _version_ | 1797211651221487616 |
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| author | A. Jahn M. Gluza F. Pastawski J. Eisert |
| author_facet | A. Jahn M. Gluza F. Pastawski J. Eisert |
| author_sort | A. Jahn |
| collection | DOAJ |
| description | Holographic quantum error-correcting codes have been proposed as toy models that describe key aspects of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. In this work, we introduce a versatile framework of Majorana dimers capturing the intersection of stabilizer and Gaussian Majorana states. This picture allows for an efficient contraction with a simple diagrammatic interpretation and is amenable to analytical study of holographic quantum error-correcting codes. Equipped with this framework, we revisit the recently proposed hyperbolic pentagon code (HyPeC). Relating its logical code basis to Majorana dimers, we efficiently compute boundary-state properties even for the non-Gaussian case of generic logical input. The dimers characterizing these boundary states coincide with discrete bulk geodesics, leading to a geometric picture from which properties of entanglement, quantum error correction, and bulk/boundary operator mapping immediately follow. We also elaborate upon the emergence of the Ryu-Takayanagi formula from our model, which realizes many of the properties of the recent bit thread proposal. Our work thus elucidates the connection among bulk geometry, entanglement, and quantum error correction in AdS/CFT and lays the foundation for new models of holography. |
| first_indexed | 2024-04-24T10:29:52Z |
| format | Article |
| id | doaj.art-1077f67f8cb14b029217ea164cf07ae9 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:29:52Z |
| publishDate | 2019-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-1077f67f8cb14b029217ea164cf07ae92024-04-12T16:46:42ZengAmerican Physical SocietyPhysical Review Research2643-15642019-11-011303307910.1103/PhysRevResearch.1.033079Majorana dimers and holographic quantum error-correcting codesA. JahnM. GluzaF. PastawskiJ. EisertHolographic quantum error-correcting codes have been proposed as toy models that describe key aspects of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. In this work, we introduce a versatile framework of Majorana dimers capturing the intersection of stabilizer and Gaussian Majorana states. This picture allows for an efficient contraction with a simple diagrammatic interpretation and is amenable to analytical study of holographic quantum error-correcting codes. Equipped with this framework, we revisit the recently proposed hyperbolic pentagon code (HyPeC). Relating its logical code basis to Majorana dimers, we efficiently compute boundary-state properties even for the non-Gaussian case of generic logical input. The dimers characterizing these boundary states coincide with discrete bulk geodesics, leading to a geometric picture from which properties of entanglement, quantum error correction, and bulk/boundary operator mapping immediately follow. We also elaborate upon the emergence of the Ryu-Takayanagi formula from our model, which realizes many of the properties of the recent bit thread proposal. Our work thus elucidates the connection among bulk geometry, entanglement, and quantum error correction in AdS/CFT and lays the foundation for new models of holography.http://doi.org/10.1103/PhysRevResearch.1.033079 |
| spellingShingle | A. Jahn M. Gluza F. Pastawski J. Eisert Majorana dimers and holographic quantum error-correcting codes Physical Review Research |
| title | Majorana dimers and holographic quantum error-correcting codes |
| title_full | Majorana dimers and holographic quantum error-correcting codes |
| title_fullStr | Majorana dimers and holographic quantum error-correcting codes |
| title_full_unstemmed | Majorana dimers and holographic quantum error-correcting codes |
| title_short | Majorana dimers and holographic quantum error-correcting codes |
| title_sort | majorana dimers and holographic quantum error correcting codes |
| url | http://doi.org/10.1103/PhysRevResearch.1.033079 |
| work_keys_str_mv | AT ajahn majoranadimersandholographicquantumerrorcorrectingcodes AT mgluza majoranadimersandholographicquantumerrorcorrectingcodes AT fpastawski majoranadimersandholographicquantumerrorcorrectingcodes AT jeisert majoranadimersandholographicquantumerrorcorrectingcodes |