Quantum Gravity
Quantum Gravity — Emergent Spacetime from Entanglement · Quantum Gravity
Reconstruct the geometry of spacetime from quantum entanglement — test whether gravity is emergent (Ryu–Takayanagi).
📋 The problem
General relativity and quantum mechanics disagree at the smallest scales. Holography (AdS/CFT, Ryu–Takayanagi: S(A)=Area/4G) suggests spacetime geometry emerges from quantum entanglement. Reconstructing the bulk from boundary entanglement tests whether gravity is emergent.
🧗 Why it's a grand challenge
We lack direct experiments; toy models are the proving ground; bulk reconstruction is an ill-posed inverse problem constrained by subtle entanglement inequalities.
🧮 Governing model
S(A) = Area(γ_A) / 4 G_N (Ryu–Takayanagi)Holographic entanglement entropy S(A)=Area(γ_A)/4G_N; reconstruct the bulk metric g_{μν} from boundary entanglement entropies of a CFT state.
Current best: Tensor-network / RT bulk reconstruction (AdS/CFT toy models)
🧭 Possible approaches
- Tensor-network and neural bulk reconstruction from boundary entanglement
- Learning the RT surface / entanglement-wedge map
- Testing reconstructions against known AdS duals
🎯 Build the benchmark
Reconstruct the bulk metric from boundary entanglement entropies with low geodesic-area error, respecting strong subadditivity.
Metric: metric_recon_err — bulk-metric reconstruction error (lower better)
Datasets to start from: AdS/CFT tensor-network entanglement corpus, Random-CFT entanglement-spectrum set
🤖 Build an AI agent to solve it
An agent that, given a boundary state's entanglement data, proposes and scores candidate bulk geometries.
Once a benchmark exists, an AI4Science agent can iterate solutions against it — every verified solution earns PWM.
This is a frontier framing page — an open problem, not yet benchmarked or verified, unlike PWM's mature computational-imaging benchmarks.