## Definition **Quantum annealing** is a physical and computational optimisation method that uses quantum mechanical effects — principally quantum tunnelling — to search for the global minimum of an objective function, in contrast to [[Simulated Annealing]], which uses thermal fluctuations. ## Mechanism Classical SA escapes energy barriers by randomly jumping *over* them (accepted with probability $\exp(-\Delta/T)$). Quantum annealing instead tunnels *through* barriers: the system is initialised in a quantum superposition of all candidate states, governed by a transverse-field Hamiltonian. As this transverse field is slowly switched off (the quantum analogue of cooling), the system is intended to settle into the ground state, which corresponds to the optimum of the objective. The process exploits two quantum phenomena: - **Quantum tunnelling** — allows transitions through energy barriers that would be thermally improbable, potentially crossing tall but thin barriers more efficiently than thermal fluctuations. - **Quantum superposition** — the system explores many configurations simultaneously rather than one at a time. ## Hardware Realisation D-Wave Systems has produced quantum annealing hardware (D-Wave 2000Q, Advantage) with thousands of superconducting qubits arranged as an Ising-model graph. Problems must be reformulated as Quadratic Unconstrained Binary Optimisation (QUBO) to run on D-Wave hardware. ## Practical Advantage — Debated Whether quantum annealing delivers a practical speed advantage over classical solvers remains actively debated: - Some studies report speed-ups on specific problem instances; others find that carefully tuned classical simulated annealing or specialised solvers match or beat D-Wave on the same benchmarks. - Noise, limited qubit connectivity, and embedding overhead reduce effective performance. - The theoretical advantage (quantum tunnelling through barriers) does not straightforwardly translate to real-world combinatorial optimisation, where landscape structure matters. As of 2026, quantum annealing has not demonstrated a clear, general-purpose advantage over the best classical optimisation methods. ## Related - [[Simulated Annealing]] — the classical thermal analogue; same high-level goal, different escape mechanism - [[Cooling Schedule]] — the classical counterpart of the transverse-field schedule in quantum annealing - [[Metropolis Acceptance Criterion]] — the classical stochastic acceptance rule that quantum tunnelling aims to improve upon - [[Combinatorial Optimization]] — the problem class both SA and quantum annealing target