Holographic Codes from Hyperinvariant Tensor Networks

• URL: http://arxiv.org/abs/2304.02732v1
• Date: Wed, 5 Apr 2023 20:28:04 GMT
• Title: Holographic Codes from Hyperinvariant Tensor Networks
• Authors: Matthew Steinberg, Sebastian Feld, Alexander Jahn
• Abstract summary: 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.
• Score: 70.31754291849292
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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