Holographic codes from hyperinvariant tensor networks

Matthew Steinberg, Sebastian Feld and Alexander Jahn ()
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Matthew Steinberg: Delft University of Technology
Sebastian Feld: Delft University of Technology
Alexander Jahn: Freie Universität Berlin

Nature Communications, 2023, vol. 14, issue 1, 1-10

Abstract: 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.

Date: 2023
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DOI: 10.1038/s41467-023-42743-z

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