OpenAI reports thermodynamic-first QAOA optimality for the SK model

For the zero-field Gaussian Sherrington–Kirkpatrick model, as system size tends to infinity first and QAOA depth then grows, the best limiting expected energy per spin approaches the Parisi ground-state value. For every accuracy, one finite depth and deterministic angles work independently of system size and disorder.

Sources for this record

What was already known

Fixed-depth thermodynamic QAOA values and concentration were known. Basso, Farhi, Marwaha, Villalonga and Zhou conjectured their increasing-depth limit reaches the Parisi optimum; fixed-instance depth optimality did not resolve this order of limits.

AI involvement AI-led

OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.

OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.

Importance Major

Proves eventual Parisi optimality of standard QAOA in the fixed-parameter thermodynamic formulation.

Limitations

No quantitative depth bound or efficient angle-selection method is claimed. The linked Lean note checks Parisi value and diffusion identities, not convergence of QAOA circuit energies.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.

Correction and publication history

2026-10-18 · publication

Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.

Read this published revision