Holographic duality between local Hamiltonians from random tensor networks

Abstract

The AdS/CFT correspondence realises the holographic principle where information in the bulk of a space is encoded at its border. We are yet a long way from a full mathematical construction of AdS/CFT, but toy models in the form of holographic quantum error correcting codes (HQECC) have replicated some interesting features of the correspondence. In this work we construct new HQECCs built from random stabilizer tensors that describe a duality between models encompassing local Hamiltonians whilst exactly obeying the Ryu-Takayanagi entropy formula for all boundary regions. We also obtain complementary recovery of local bulk operators for any boundary bipartition. Existing HQECCs have been shown to exhibit these properties individually, whereas our mathematically rigorous toy models capture these features of AdS/CFT simultaneously, advancing further towards a complete construction of holographic duality.

arXiv comment42 pages, 4 figures. v4: updated to published version, expanded introduction and new figure demonstrating simulation composition

References in corpus (28)

• The World as a Hologram
• Quantum corrections to holographic entanglement entropy
• Entanglement Renormalization and Holography
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Bulk Locality and Quantum Error Correction in AdS/CFT
• Holography from Conformal Field Theory
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Dimensional Reduction in Quantum Gravity
• Holographic duality from random tensor networks
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• Aspects of generic entanglement
• The Gravity Dual of Renyi Entropy
• Emergent Spacetime and Holographic CFTs
• Flat entanglement spectra in fixed-area states of quantum gravity
• Bidirectional holographic codes and sub-AdS locality
• Standard forms of noisy quantum operations via depolarization
• Universal Quantum Hamiltonians
• Entanglement in the stabilizer formalism
• Multipartite Entanglement in Stabilizer Tensor Networks
• Unconditionally Secure Key Distribution In Higher Dimensions By Depolarization
• The Church of the Symmetric Subspace
• Large Deviation Bounds for k-designs
• Exploring the Tensor Networks/AdS Correspondence
• Toy Models of Holographic Duality between local Hamiltonians
• Absolutely Maximally Entangled States: Existence and Applications
• Dynamics for holographic codes
• Discrete Gravity on Random Tensor Network and Holographic Rényi Entropy
• Translationally-Invariant Universal Quantum Hamiltonians in 1D

Cited by in corpus (7)

• Fun with replicas: tripartitions in tensor networks and gravity
• Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits
• Gauging the bulk: generalized gauging maps and holographic codes
• Multipartite edge modes and tensor networks
• Background independent tensor networks
• Universal Spreading of Conditional Mutual Information in Noisy Random Circuits
• Security of quantum position-verification limits Hamiltonian simulation via holography