Bulk-boundary correspondence from hyper-invariant tensor networks
arXiv:2409.02029 · doi:10.1103/PhysRevD.111.026006
Abstract
We introduce a tensor network designed to faithfully simulate the AdS/CFT correspondence, akin to the multi-scale entanglement renormalization ansatz (MERA), following hyper-invariant 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.
21 pages, 12 figures
References in corpus (37)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Area laws for the entanglement entropy - a review
- Geometric and Renormalized Entropy in Conformal Field Theory
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
- Holographic duality from random tensor networks
- Optimal Creation of Entanglement Using a Two--Qubit Gate
- A geometric theory of non-local two-qubit operations
- Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
- Tensor network states and geometry
- Quantum dynamics as a physical resource
- Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices
- Entanglement renormalization, scale invariance, and quantum criticality
- A scheme for direct detection of qubit-environment entanglement generated during qubit pure dephasing
- Particle-Time Duality in the Kicked Ising Chain I: The Dual Operator
- Particle-Time Duality in the Kicked Ising Chain II: Applications to the Spectrum
- Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
- Consistency Conditions for an AdS/MERA Correspondence
- Characterization of non-local gates
- Entanglement and quantum combinatorial designs
- Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity
- Thirty-six entangled officers of Euler: Quantum solution to a classically impossible problem
- Hyper-invariant tensor networks and holography
- Exploring the Tensor Networks/AdS Correspondence
- Calderbank-Steane-Shor Holographic Quantum Error Correcting Codes
- Algorithms for entanglement renormalization: boundaries, impurities and interfaces
- Tensor network and (-adic) AdS/CFT
- Can local dynamics enhance entangling power?
- Central charges of aperiodic holographic tensor network models
- Majorana dimers and holographic quantum error-correcting codes
- Bipartite unitary gates and billiard dynamics in the Weyl chamber
- Holographic Codes from Hyperinvariant Tensor Networks
- Conformal Properties of Hyperinvariant Tensor Networks
- Boundary theories of critical matchgate tensor networks
- Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations
- Dual unitaries as maximizers of the distance to local product gates
- Dual-isometric Projected Entangled Pair States