Adiabatic QC (Farhi 2000): start in ground state of H_0 = -Σσˣᵢ (easy), slowly evolve to H_P (hard problem). Adiabatic theorem: stay in ground state if T ≫ 1/Δ²_min. The minimum spectral gap Δ_min is the bottleneck — it can be exponentially small for NP-hard problems. D-Wave machines implement this for Ising optimization.