A Machine-Verified Proof of a Quantum-Optimization Conjecture
We report a machine-verified resolution of a problem open for over a decade in quantum optimization: the Farhi, Goldstone and Gutmann (FGG) conjecture that depth-$p$ Quantum Approximate Optimization Algorithm (QAOA) on the ring of disagrees attains approximation ratio $(2p+1)/(2p+2)$ exactly. We found the proof using a large language model, Claude Fable 5, and verified its correctness end-to-end by the Lean 4 proof assistant. Our methodology includes several ingredients: building on a substantial Lean library of quantum information, we formalized the QAOA components and the known parts of the problem, and reduced the conjecture to a single open mathematical statement. The model was then h...
| Authors | Uri Kol, Maor Ben-Shahar, Kfir Sulimany et al. |
|---|---|
| Primary category | quant-ph |
| Published | 29 June 2026 |
| Last updated at source | 29 June 2026 |
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