Part 6 · hardware decision
The local task is classically solvable, yet a quantum processor might still reach a 1%-accurate answer sooner. That narrower claim is measurable.
Why only two measurement settings are needed
All thirteen X probes can be measured in one X-basis family. The thirteen Z and sixteen ZZ probes share a Z-basis family. This grouping keeps the shot cost far below a separate execution for every observable.
The PEA/ZNE transfer estimate
A separately validated 51-qubit Floquet workflow used noise factors 1.0, 1.3 and 1.6, 1,024 shots per factor, twirling, measurement mitigation and fresh learning of up to three layer-noise models. It consumed 41 charged QPU seconds. Early depths matched the classical reference well; the full eight-cycle accuracy gate did not pass.
Transferred to this shallower two-layer task, the estimate is 25–26 QPU seconds at the original statistics and roughly 31–45 seconds if target shots are increased toward 1% statistical precision. Against the current 393-second high-precision classical route, that is a possible factor of 8.7–12.7 in charged QPU time.
| Requirement | Pass condition |
|---|---|
| Accuracy | Less than 1% preregistered total error, including systematic effects |
| Classical fairness | Optimize the lightcone/MPS route for the same 1% tolerance |
| Quantum cost | Count learning, mitigation and execution; report queue time separately |
| Coverage | Evaluate all 42 frozen observables, not a favorable subset |
| Reproducibility | Freeze the ISA circuit hash, shots, backend and mitigation configuration before submission |
IBM describes PEA as a ZNE amplification method that first learns a twirled layer-noise model and then injects scaled noise before extrapolation. It can improve utility-scale expectation values, but it cannot guarantee an unbiased answer.
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.