Holographic codes from hyperinvariant tensor networks.
Nat Commun
; 14(1): 7314, 2023 Nov 11.
Article
in En
| MEDLINE
| ID: mdl-37951990
ABSTRACT
Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code's logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery. However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states. In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states. Furthermore, these codes exhibit a state-dependent breakdown of complementary recovery as expected from AdS/CFT under small quantum gravity corrections.
Full text:
1
Collection:
01-internacional
Database:
MEDLINE
Language:
En
Journal:
Nat Commun
Journal subject:
BIOLOGIA
/
CIENCIA
Year:
2023
Document type:
Article
Affiliation country:
Netherlands