The Basso-Farhi-Marwaha-Villalonga-Zhou conjecture: QAOA attains the Sherrington-Kirkpatrick ground-state energy as depth grows

Theorem 1.1: $\lim_{p\to\infty}Q_p=P_*$ for the zero-field SK model; for every $\varepsilon>0$ some finite depth and deterministic angles, independent of $n$ and the disorder, reach expected energy per spin $\ge P_*-\varepsilon$ in the limit $n\to\infty$ taken first, with the standard cost Hamiltonian and transverse-field mixer. It also gives leading-order optimal expected MaxCut on large-degree random regular graphs (size before degree). Not given: any depth bound, finite-size estimate, efficient angle selection, or concentration beyond expectation. The companion proves full support on $[0,1)$ of zero-temperature Parisi minimizers, a result H.-B. Chen had already posted (arXiv 2607.18032), as the companion acknowledges.

Theorem 1.1: $\lim_{p\to\infty}Q_p=P_*$ for the zero-field SK model; for every $\varepsilon>0$ some finite depth and deterministic angles, independent of $n$ and the disorder, reach expected energy per spin $\ge P_*-\varepsilon$ in the limit $n\to\infty$ taken first, with the standard cost Hamiltonian and transverse-field mixer. It also gives leading-order optimal expected MaxCut on large-degree random regular graphs (size before degree). Not given: any depth bound, finite-size estimate, efficient angle selection, or concentration beyond expectation. The companion proves full support on $[0,1)$ of zero-temperature Parisi minimizers, a result H.-B. Chen had already posted (arXiv 2607.18032), as the companion acknowledges.