Quantum annealing is an analog quantum computing paradigm that solves optimization problems by exploiting quantum tunneling. The system starts in the ground state of a simple Hamiltonian (all qubits in superposition) and slowly evolves toward a problem-specific Hamiltonian whose ground state encodes the optimal solution. During this evolution, quantum tunneling allows the system to pass through energy barriers that would trap classical optimization algorithms, potentially finding better solutions.
D-Wave Systems is the primary commercial quantum annealing company, with processors exceeding 5,000 qubits — far more than any gate-based quantum computer. D-Wave's systems are purpose-built for optimization and cannot run general quantum algorithms like Shor's or Grover's. Their Advantage processors use a Pegasus connectivity graph where each qubit connects to 15 others, and problems must be embedded into this topology. D-Wave introduced gate-model capabilities with their Advantage2 processor line, signaling a potential convergence of approaches.
The debate over quantum speedup from annealing is long-running and unresolved. D-Wave has demonstrated that their processors can solve certain structured optimization problems faster than specific classical algorithms, but critics point out that custom-designed classical heuristics and simulated annealing often match or beat the quantum annealer when given equal development effort. The consensus is that quantum annealing has not yet demonstrated unambiguous quantum advantage for practical optimization problems. Nevertheless, companies including Volkswagen, DENSO, and various financial firms have explored D-Wave systems for logistics, scheduling, and portfolio optimization, finding them useful in some niche applications.