Quantum Annealing

Quantum annealing seeks the ground state of an optimization problem by slowly evolving from an easy Hamiltonian to the problem Hamiltonian, using quantum tunnelling to escape local minima.

Model

adiabatic / analog

Targets

QUBO / Ising problems

Contrast

gate-model QAOA is the digital cousin

What it does

Start in the ground state of a simple transverse-field Hamiltonian, then adiabatically turn on the problem Hamiltonian. If done slowly enough, the system stays in the ground state — which now encodes the optimal solution. Tunnelling can cross barriers that trap classical annealers.

Where it's used

Combinatorial optimization on specialized hardware; useful framing for design-space and scheduling problems.

In code (Qiskit)

# Map problem to Ising couplings J_ij, h_i; anneal transverse field -> 0