Hamiltonian
H(s) = −A(s)∑ σˣᵢ + B(s)∑ Jᵢⱼσᶻᵢσᶻⱼ
s goes 0→1 during anneal.
A(s)→0: Transverse field (quantum) turns off
B(s)→1: Problem Hamiltonian turns on
At s=0: quantum tunneling lets the particle exist simultaneously in all minima. As s→1 it must "choose" one.
Adiabatic theorem: if annealing is slow enough relative to the minimum gap, the system stays in the ground state.
Tunneling vs Thermal
Classical SA jumps barriers via thermal fluctuations — can get stuck in local minima.
Quantum annealing tunnels through barriers — potentially better for tall, thin barriers.
D-Wave machines use quantum annealing for combinatorial optimization. The quantum advantage question is still open for practical problem instances.
Quantum finds global: —
Classical: —