Strong anchors + weak weaving: a two-boundary SYK / GJW-inspired protocol for traversable wormholes (toy model)

I explored a simple conceptual split:

• Strong entanglement → “anchors” that primarily fix the geometry of the two ends
• Weak entanglement → “weaving” that controls the connectivity of the throat

I mapped this onto a two-boundary SYK model with a Gao–Jafferis–Wall (GJW)-type coupling and checked it with exact diagonalization (N=4 Majorana per side). The results are consistent with the expected behavior of a weakly coupled traversable wormhole in the AdS₂/JT limit. This is strictly a toy model.

Motivation

ER=EPR (Maldacena & Susskind, 2013) tells us that entanglement is dual to a non-traversable Einstein–Rosen bridge. Traversability requires an effective negative-energy injection. Gao, Jafferis & Wall (2017) showed that a carefully chosen double-trace deformation between the two boundaries can produce such a negative-energy shockwave in the bulk.

I asked whether one can separate the roles of entanglement more cleanly:

• Strong, local entanglement mainly sets the geometry of the two “mouths” (anchors).
• Weaker, cross-boundary entanglement mainly controls the connectivity and traversability of the throat (weaving).

Model

Two-boundary SYK Hamiltonian (Kitaev 2015; Sachdev & Ye 1993):

(which corresponds to a double-trace deformation in the boundary CFT, following the GJW protocol). μ is the weak-weaving strength.

• μ=0 : two independent thermal systems connected by a non-traversable ER bridge.
• Small μ>0 : negative-energy shockwave opens a temporary throat → signal can cross.
• Large μ : the two systems thermalize into a single state; the geometric notion of a wormhole disappears.

Numerical check (exact diagonalization)

I constructed the eight Majorana operators via Pauli strings on a 16-dimensional Hilbert space and computed the infinite-temperature cross-boundary correlator

Quantum-simulation sketch (NISQ)

1. Prepare an approximate thermofield-double state (strong anchors).
2. Encode a qubit state on the left boundary.
3. Evolve under a Trotterized version of Hweak Hweak​ (cross-boundary XX/YY-type gates).
4. Decode on the right boundary and measure fidelity.

A useful experimental fingerprint: the sign of μ . Positive μ \mu μ should enhance the signal (negative-energy shockwave); negative μ \mu μ should suppress it further. Ordinary gate noise is usually sign-insensitive.

Important limitations

• This is a 0+1D toy model in the AdS₂/JT limit.
• Macroscopic traversable wormholes still require macroscopic amounts of negative energy; GJW only provides an effective negative-energy shockwave in the bulk dual.
• Our universe is de Sitter, not anti-de Sitter. Extending the construction to dS is non-trivial.
• Exact diagonalization is limited to very small N.
• Decoherence and gate errors will swamp the signal unless careful error mitigation and the sign-sensitivity test are used.
• Nothing here claims that we can build a macroscopic wormhole in the laboratory.

Open questions

• Can one make the weak-weaving term more realistic (e.g., only a few cross terms)?
• How does the critical μc \mu_c μc​ scale with N?
• Is there a clean tensor-network / MERA picture of the strong-anchor + weak-weaving split?
• What is the best way to diagnose “geometric” versus “purely quantum-information” effects on a real quantum processor?

I’m posting this mainly to get criticism. Constructive comments, references I missed, or suggestions for cleaner numerics/circuits are very welcome.

(If anyone wants the small-N ED script or a more detailed circuit sketch, just ask.)