Tensor Network Toy Models of Holographic Dualities: Locality and Causality
summary
Combines holographic quantum error-correcting codes with Hamiltonian simulation to produce a bulk→boundary mapping that preserves encoding, entanglement scaling and produces a geometrically local boundary Hamiltonian after simulation; uses random stabilizer tensors so Pauli rank is preserved and avoids exponential gadget blowup, yielding a local simulator on about n polylog n qudits. Adds depth-dependent Hamiltonian scaling to reproduce AdS time dilation and sensible butterfly velocities. Builds work but still lacks genuine gravity, exact conformal symmetry, and a simulator strong enough to force an exponential-position-crypto break.
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chapters (11)
- 0:00Introduction to AdS/CFT
- 2:23Holographic error correction
- 7:28Tensor network toy models
- 12:15Entanglement and geometry
- 13:57Hamiltonian simulation
- 21:51Stabilizer tensor networks
- 27:20Dynamics and time dilation
- 29:53Causal structure and signaling
- 38:04Position-based cryptography
- 43:11Conclusion and open questions
- 51:57Q&A session
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