The Quantum Approximate Optimization Algorithm (QAOA) alternates between problem Hamiltonian H_C and mixer H_B = -Σσ_x with angles (γ,β). Explore how the landscape of ⟨H_C⟩ changes with circuit depth p and problem hardness.
QAOA p=1: landscape is smooth, findable by gradient descent. Higher p: more complex landscape, local minima proliferate. MaxCut approximation ratio approaches 1 as p→∞. Farhi et al. 2014 showed p=1 QAOA achieves ≥0.6924 on 3-regular graphs.