Adiabatic optimization: turning off quantum fluctuations to find classical ground state
s = 0.00 | Γ = 1.00 | Gap = —
Quantum annealing: H(s) = −Γ(s)Σσˣᵢ − J(s)Σσᶻᵢσᶻᵢ₊₁, where s: 0→1 is the annealing parameter.
Start: Γ=1, J=0 (trivial transverse-field ground state |+⟩^⊗L).
End: Γ=0, J=1 (classical Ising ground state |↑↑...⟩ or |↓↓...⟩).
Adiabatic theorem: if annealing is slow enough (T ≫ 1/gap²), the system stays in the ground state.
The minimum gap (avoided crossing) determines the required annealing time.
Top: energy spectrum vs s. Middle: spin configuration during anneal. Bottom: success probability vs T.