Bulk-boundary correspondence from hyperinvariant tensor networks

We introduce a tensor network designed to faithfully simulate the $\mathrm{AdS}/\mathrm{CFT}$ correspondence, akin to the multiscale entanglement renormalization ansatz (MERA), following hyperinvariant tensor network. The proposed construction integrates bulk indices within the network architecture to uphold the key features of the HAPPY code, including complementary recovery. This framework accurately reproduces the boundary conformal field theory's (CFT) two- and three-point correlation functions, while considering the image of any bulk operator. Furthermore, we provide an explicit methodology for calculating the correlation functions in an efficient manner. Our findings highlight the physical aspects of the relation between bulk and boundary within the tensor network models, contributing to the understanding and simulation of holographic principles in quantum information.