July 31, 2023 to August 4, 2023
Perimeter Institute for Theoretical Physics
America/Toronto timezone

Talk 106 - Holographic Codes from Hyperinvariant Tensor Networks

Aug 1, 2023, 10:00 AM
PI/1-100 - Theatre (Perimeter Institute for Theoretical Physics)

PI/1-100 - Theatre

Perimeter Institute for Theoretical Physics



Alexander Jahn (Free University of Berlin)


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.

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