Adiabatic Quantum Computation

Visualize quantum annealing: H(s) = (1-s)H₀ + s·H_P interpolates from easy to problem Hamiltonian. The energy gap closes near a quantum phase transition — too fast = diabatic errors.

Hamiltonian Parameters

Qubits n 3 Gap min Δ 0.20 Disorder J 0.50 Anneal speed v 0.005

Quantum phase: Initial

Adiabatic theorem:
If swept slowly (v ≪ Δ²), system stays in ground state.

Gap: Δ(s) = E₁(s) - E₀(s)
Closing gap → quantum phase transition → diabatic excitation.

Success: P(ground) = |⟨ψ(T)|E₀(T)⟩|²

Landau-Zener: P_err ≈ exp(-πΔ²/2v)