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arXiv · 2304.02732

Holographic Codes from Hyperinvariant Tensor Networks

Matthew Steinberg·Sebastian Feld·Alexander Jahn
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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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Matthew Steinberg, Sebastian Feld, Alexander Jahn. 2023-04-05. Holographic Codes from Hyperinvariant Tensor Networks. https://doi.org/10.1038/s41467-023-42743-z

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