PIRSA:23080002 Conference Quantum Fields and Strings Quantum Information Quantum Foundations

DOI10.48660/23080002

Conference/School: It from Qubit 2023

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

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

@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}}
}

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.

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