QAOA applies alternating phase (cost) and mixing (driver) unitaries: |ψ⟩ = U_B(β_p)U_C(γ_p)…U_B(β_1)U_C(γ_1)|+⟩^n. Maximizes ⟨C⟩ = expected cut value on a graph.
Farhi et al. (2014): QAOA with p layers achieves approximation ratio ≥ 1/2 for Max-Cut. As p→∞ it approaches exact optimization. Energy landscape scanned over (γ,β) space for depth p=1.