Quantum annealing

In plain language

Many practical puzzles, such as scheduling jobs in a factory or arranging parts efficiently, have so many possible answers that checking them one by one is impossible. A classical method called simulated annealing searches for good answers by making large changes at first and then gradually settling, a little like metal cooling into a stable shape. Quantum annealing follows the same idea but uses quantum effects to help the search move between answers. Special-purpose quantum annealers, such as those built by D-Wave, are designed to run this process on problems that can be written in a particular form.

The open question is whether this gives a real advantage over the best classical computers. Early tests on random problems did not show a clear speed-up. In 2025, D-Wave reported a simulation of magnetic materials that it said no classical computer could match in a reasonable time. Classical researchers have since shown that other methods can match, and in some cases beat, the annealer on a similar simulation. In one pilot study on a factory scheduling problem, a hybrid solver that mixes quantum and classical steps did best at medium problem sizes, but the gains faded on large problems.

Technical explanation

Quantum annealing encodes a problem as the lowest-energy state of an Ising model, a network of binary spins with pairwise couplings. The processor starts the qubits in a simple quantum state, adds a transverse field that makes them fluctuate, and then slowly lowers that field while the problem term takes over. Kadowaki and Nishimori introduced this approach in 1998 by adding quantum fluctuations to the simulated annealing process for optimisation problems. In practice, devices are noisy and have limited precision when setting couplings, and the sources reviewed here treat these limits as a central part of any performance test.

Quantum annealers are also used to simulate physical systems. In the 2025 Science paper by King and colleagues, D-Wave's superconducting annealing processors were used to generate the dynamics of spin glasses, a model for certain disordered magnetic materials. The classical comparison relies on tensor networks, which represent quantum states as networks of smaller tensors. Entanglement grows during a time evolution, so the bond dimension needed for accuracy also grows, which makes long simulations expensive. Tindall and colleagues describe a lattice-specific tensor-network method with belief propagation that is scalable in two and three dimensions and was used to check Kibble-Zurek physics on systems of hundreds of qubits.

The disagreement is about scope and settings. Classical results depend on parameters such as bond dimension, and reported comparisons differ by lattice geometry: the Flatiron team's method reportedly had lower error than the annealer on cylindrical and diamond lattices and similar error on cubic lattices at a fixed annealing time. D-Wave argues that the classical work covers only a subset of its benchmark, including the largest three-dimensional geometries. For optimisation, the best-documented evidence so far shows annealers that are competitive on small or intermediate instances, with classical heuristics catching up as problems grow.

What the evidence says

Each statement is typed by the strength of its evidence and linked to the source that supports it.

Limitations and open problems

• On random spin glass instances, a 503-qubit D-Wave Two showed no evidence of quantum speedup when the full dataset was considered, and results on subsets of instances were inconclusive (Rønnow and colleagues, 2014).
• In a paint-shop scheduling study, annealer performance approached that of a simple greedy algorithm as problem size grew, and the hybrid solver was strongest at intermediate sizes (Yarkoni and colleagues, 2021; preprint).
• The 2025 beyond-classical simulation claim is contested. Classical tensor-network results match or beat the annealer on some lattices, while D-Wave says these results do not reproduce the full benchmark.
• Classical results depend on settings. The cylindrical-lattice advantage depends on the bond dimension being large enough, and cubic lattices showed no clear winner at a fixed annealing time (as reported by Physics World).
• Vendor-reported figures for real deployments were not checked against independent sources in this profile, and the sources reviewed here do not give verified speed-up factors on practical problems.

Possible future uses

Timeline

1. 1998Kadowaki and Nishimori introduce quantum annealing by adding quantum fluctuations to simulated annealing for optimisation problems. Sources: [6]
2. 2014Rønnow and colleagues report no evidence of quantum speedup for a D-Wave Two device with up to 503 qubits when the full random spin glass dataset is considered. Sources: [5]
3. Sept 2021Yarkoni and colleagues post a preprint comparing D-Wave 2000Q and Advantage processors with classical and hybrid solvers on a multi-car paint shop problem. Sources: [7]
4. 11 Apr 2025King and colleagues, with D-Wave authors, report in Science that a quantum annealer generates spin-glass dynamics that classical approximations cannot match in a reasonable time. Sources: [1]
5. May 2026D-Wave publicly disputes the classical result, arguing that it covers only part of the 2025 benchmark. Sources: [4]
6. 21 May 2026Tindall and colleagues publish a classical tensor-network method in Science that matches or beats the annealer on some lattice geometries. Sources: [2], [3]

Futures this could help bring about

How far away?

Quantum machines beating supercomputers on real problems

Science demonstrated · 5 of 7 steps done

Glossary

Quantum annealing

A method that finds low-energy answers to a problem by starting from a simple quantum state and slowly moving the system toward a state that encodes the problem.

Simulated annealing

A classical search method that makes large random changes at first and then gradually makes smaller ones, to reach good answers without getting stuck.

Spin glass

A disordered magnetic material in which competing interactions make many arrangements of the spins almost equally stable.

Tensor network

A way of representing a quantum state as a network of smaller linked arrays, which can make some quantum systems cheaper to simulate on classical computers.

Sources

1. peer reviewed paper
   Beyond-classical computation in quantum simulation
   Andrew D. King, Alberto Nocera, Marek M. Rams et al.. Science, 11 Apr 2025. DOI: 10.1126/science.ado6285. Accessed 21 Oct 2026.
2. peer reviewed paper
   Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
   Joseph Tindall, Antonio Francesco Mello, Matthew Fishman et al.. Science, 21 May 2026. DOI: 10.1126/science.adx2728. Accessed 21 Oct 2026.
3. news
   No quantum advantage (yet) in the world of tensor networks
   Nohora Hernández. Physics World, 21 Aug 2026. Accessed 21 Oct 2026.
4. news
   D-Wave Systematically Rebuts Flatiron Claims, Reaffirming Beyond-Classical Simulation Milestones
   Quantum Computing Report, 26 May 2026. Accessed 21 Oct 2026.
5. peer reviewed paper
   Defining and detecting quantum speedup
   Troels F. Rønnow, Zhihui Wang, Joshua Job et al.. Science, 2014. DOI: 10.1126/science.1252319. Accessed 21 Oct 2026.
6. peer reviewed paper
   Quantum Annealing in the Transverse Ising Model
   Tadashi Kadowaki, Hidetoshi Nishimori. Physical Review E, 1998. Accessed 21 Oct 2026.
7. preprint
   Multi-car paint shop optimization with quantum annealing
   Sheir Yarkoni, Alex Alekseyenko, Michael Streif et al.. arXiv (accepted to IEEE QCE21), Sept 2021. Accessed 21 Oct 2026.

Revision history

4 changes since this profile was created.