Steinberg Matthew, Feld Sebastian, Jahn Alexander
QuTech, Delft University of Technology, 2628, CJ, Delft, The Netherlands.
Quantum and Computer Engineering Department, Delft University of Technology, 2628, CD, Delft, The Netherlands.
Nat Commun. 2023 Nov 11;14(1):7314. doi: 10.1038/s41467-023-42743-z.
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.
全息量子纠错码是诸如反德西特/共形场论（AdS/CFT）对应等体/边界对偶性的模型，其中高维体几何与码的逻辑自由度相关联。先前基于张量网络的离散全息码已经重现了连续统AdS/CFT预期的一般码性质，例如互补恢复。然而，此类张量网络的边界态通常并不表现出CFT边界态预期的关联函数。在这项工作中，我们表明，一类新的精确全息码，将先前提出的超不变张量网络扩展为量子码，产生了正确的边界关联函数。这种方法在体中的逻辑态与边界态的临界重整化群流之间产生了一个字典。此外，正如在小量子引力修正下AdS/CFT所预期的那样，这些码表现出与状态相关的互补恢复破坏。
