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.

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

References in corpus (4)

• Holography from Conformal Field Theory
• Aspects of generic entanglement
• Entanglement in the stabilizer formalism
• Translationally-Invariant Universal Quantum Hamiltonians in 1D

Cited by in corpus (7)

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