Part 4 · exact local results
The global circuit has 61 qubits, but the requested local outputs only depend on their backwards causal cones. That changes the answer completely.
Depth one
All 42 probes are exactly solvable by small causal-lightcone statevectors. An independent, untruncated Majorana propagation agrees on all 29 common Z and ZZ probes to machine precision. For this task, depth one is decisively classical.
Depth two
The cones now contain 6 to 32 qubits. Forty-one observables have cones of at most 24 qubits and were computed exactly in about 272 seconds in the first serial run. Only the central probe ZZ0,1 needs 32 qubits. A graph-aware local MPS gives 0.0192082768484 identically at χ = 256 and χ = 512.
| Component | Method | Measured time |
|---|---|---|
| 41 local cones | Exact statevectors | about 272 s |
| Central 32-qubit cone | First converged MPS at χ = 256 | about 172 s |
| Current high-precision route | Exact cones plus independent converged MPS | about 393 s |
The public repository contains all 42 values, cone sizes, methods and convergence diagnostics. The 393-second comparison is a development-machine measurement, not an optimized classical lower bound.
Sources and reproducibility
- Bose et al., A Spin Entanglement Witness for Quantum Gravity
- Marletto & Vedral, Gravitationally Induced Entanglement
- Sabín, Digital quantum simulation of quantum gravitational entanglement
- Pastawski et al., Holographic quantum error-correcting codes
- IBM Quantum documentation: ZNE and PEA
- Public code, numerical reports and full 42-value table on GitHub
Project status: 14 August 2026. Numerical values come from the frozen public research artifacts; claim boundaries are deliberately preserved.