Talk 106 - Holographic Codes from Hyperinvariant Tensor Networks

          @misc{ scivideos_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 for Theoretical Physics},
            year = {2023},
            month = {aug},
            note = {PIRSA:23080002 see, \url{https://scivideos.org/index.php/pirsa/23080002}}
          }
          

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.