H = -Γ(t)Σσ^x_i - J Σσ^z_i σ^z_j. As transverse field Γ → 0, quantum fluctuations freeze out, leaving (ideally) the ground state.
Quantum annealing (Kadowaki-Nishimori 1998): start with H = -Γ_0 Σσ^x (all spins in + x superposition), slowly ramp to H = -J Σσ^z σ^z (Ising problem). Adiabatic theorem guarantees ground state if Γ decreases slowly enough relative to the gap.