Algorithms
Quantum Annealing
A method that finds low-energy states of a problem by slowly changing a quantum system from a simple Hamiltonian to a problem-encoding one.
Definition
Quantum annealing is a way to solve optimization problems by letting a physical quantum system settle into its lowest-energy state. The problem is encoded into the interactions among many qubits, and the system starts in a simple quantum state that is gradually transformed into the problem. If the transformation is slow enough, the system ends in the best answer, or a good approximation. D-Wave builds commercial machines of this type with thousands of qubits.
In depth
Quantum annealing is a different style of quantum computing from the gate model. There are no circuits or discrete gates: the user sets biases and couplings and starts a physical process that takes microseconds. This makes devices simpler to scale in qubit count, and D-Wave's Advantage2 has more than 4,400 qubits, but it limits the problems to optimization and sampling, and the qubit counts are not comparable with gate-model counts.
Evidence about advantage is mixed. Experiments showed that for specially designed problems, annealers can outperform simulated annealing by large factors, and a 2025 D-Wave paper claimed beyond-classical results in simulating magnetic materials. Other studies find that quantum Monte Carlo and tensor network methods match annealers on many problems, and no broad advantage on commercial optimization problems has been established. Whether tunneling plays the key role is an active research question.
In practice, users encode problems as QUBOs, quadratic unconstrained binary optimization problems, embed them into the hardware graph, run thousands of anneals, and take the best sample. Hybrid solvers split large problems into pieces, which has produced most of the industrial pilots in logistics, scheduling, and finance.
Technical Definition
Quantum annealing evolves under H(s) equal to A(s) times a transverse-field driver Hamiltonian plus B(s) times a problem Ising Hamiltonian, with s going from 0 to 1. The adiabatic theorem says that, for slow enough evolution relative to the minimum spectral gap, the system stays in its ground state. Real devices are noisy and operate at finite temperature, so they act as heuristic samplers.
Visual Explanation: An Analogy
Imagine pouring water over a rough landscape and letting it settle into the lowest valley. A classical method might need to push the water uphill to escape shallow dips, but the quantum version can also seep through the walls, which is the tunneling picture of annealing.
Key facts
| Item | Detail |
|---|---|
| Origin | Kadowaki and Nishimori, 1998; first commercial machine, D-Wave One, 2011 |
| Largest machine | D-Wave Advantage2, more than 4,400 qubits |
| Problem form | Ising or QUBO models |
| Run time | Microseconds per anneal |
| Open question | Whether it gives practical advantage over classical solvers |
Where the idea comes from
The idea of using quantum fluctuations in optimization appeared in the late 1980s, and Kadowaki and Nishimori's 1998 paper is the standard reference. D-Wave Systems commercialized it starting in 2011, and the technology has been tested in many industry pilots.
Real-World Use Cases
- Scheduling, routing, and portfolio optimization pilots.
- Sampling from Boltzmann distributions for machine learning.
- Simulating magnetic and spin-glass systems.
- Benchmarking quantum and classical heuristics.
How it differs from related ideas
- Gate-model computers can run general algorithms, while annealers target optimization.
- Simulated annealing uses thermal hops, while quantum annealing uses quantum fluctuations.
- Adiabatic quantum computation is the idealized version with guarantees, and annealing is its noisy hardware implementation.
Common Misconceptions
- Annealers do not try all solutions at once. They settle into low-energy states.
- Thousands of annealing qubits do not equal a thousand gate-model qubits.
- A reported speedup relative to simulated annealing is not proof of advantage over the best classical solver.
Frequently asked questions
What is quantum annealing?
An optimization method that uses a quantum system's evolution from a simple state to a problem-encoding state to find low-energy solutions.
Who makes quantum annealers?
D-Wave Systems is the main commercial maker.
Does it solve NP-hard problems quickly?
No. It is a heuristic with no proven polynomial-time guarantee.
Related Terms
Keep exploring
- Algorithm: Quantum Annealing
- Algorithm: Adiabatic Quantum Computation
- Algorithm: Quantum Approximate Optimization Algorithm (QAOA)
- Hardware: D-Wave Advantage2
- Industry: Quantum Computing for Logistics
- Industry: Quantum Computing for Manufacturing