OpenAI · 281-01 · 2026-09-25 · Mathematical physics
QAOA attains the SK ground-state energy in the thermodynamic-first limit
preprints/QAOA-attains-the-SK-ground-state-energy-in-the-thermodynamic-first-limit-September-25-2026
Family 281. QAOA optimality for the SK model.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves that QAOA approaches the ground-state energy of the Gaussian zero-field Sherrington–Kirkpatrick model when system size tends to infinity before circuit depth. For every accuracy, finite depth and deterministic angles independent of size and disorder achieve the required limiting expected energy per spin. This also yields leading-order optimal expected MaxCut values on large-degree random regular graphs, with size tending to infinity before degree.
We prove that the Quantum Approximate Optimization Algorithm (QAOA) approaches the ground-state energy per spin of the Gaussian zero-field Sherrington–Kirkpatrick model when system size tends to infinity first and circuit depth then increases. For every accuracy, some finite depth and deterministic angles, independent of system size and disorder, achieve that accuracy in the limiting expected energy per spin using the standard cost Hamiltonian and transverse-field mixer. This proves the eventual Parisi-optimality conjecture of Basso, Farhi, Marwaha, Villalonga, and Zhou in its fixed-parameter thermodynamic formulation. We give no quantitative bound on the required depth or efficient angle-selection procedure.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 281: QAOA attains the SK optimum in the thermodynamic-first limit. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.