# Talk 106 - Holographic Codes from Hyperinvariant Tensor Networks

### APA

Jahn, A. (2023). Talk 106 - Holographic Codes from Hyperinvariant Tensor Networks. Perimeter Institute. https://pirsa.org/23080002

### MLA

Jahn, Alexander. Talk 106 - Holographic Codes from Hyperinvariant Tensor Networks. Perimeter Institute, Aug. 01, 2023, https://pirsa.org/23080002

### BibTex

@misc{ pirsa_PIRSA:23080002, doi = {10.48660/23080002}, url = {https://pirsa.org/23080002}, author = {Jahn, Alexander}, keywords = {Quantum Fields and Strings, Quantum Information, Quantum Foundations}, language = {en}, title = {Talk 106 - Holographic Codes from Hyperinvariant Tensor Networks}, publisher = {Perimeter Institute}, year = {2023}, month = {aug}, note = {PIRSA:23080002 see, \url{https://pirsa.org}} }

Free University of Berlin

**Collection**

Talk Type

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.