Quantum annealing and adiabatic optimisation
Algorithms and benchmarks / Optimisation
Special-purpose machines encode an optimisation problem as the lowest-energy state of a network of coupled qubits and let the system settle into it. Adiabatic quantum computation is the gate-free model behind it.
- Era
- Analogue or special-purpose
- Problem class
- Optimisation
- Speedup
- Problem-dependent and debated; King et al. (2023) report critical dynamics that support a scaling advantage in reducing energy with annealing time over analogous Monte Carlo dynamics in 3D spin glasses.
How it works
The system starts in the easy ground state of a simple Hamiltonian and is slowly changed into the problem Hamiltonian; if the change is slow compared with the smallest energy gap, it ends near the solution (Farhi et al. 2000).
Typical use cases
- Scheduling, routing, energy grid planning and portfolio selection, often in hybrid quantum-classical solvers.
Documented use cases on related problems
From the use case directory; the sources of these cases may use other methods than this one.
- Bus routing with a quantum computer during Web Summit in Lisbon (Volkswagen and CARRIS)
- Hybrid quantum scheduling in a liquid-filling plant (BASF and D-Wave)
- Placement of grid-scale batteries with quantum and quantum-inspired algorithms (Iberdrola and Multiverse)
- Dynamic investment portfolio optimisation on quantum platforms (BBVA and Multiverse)
Resource estimates
No resource estimate with stated assumptions was verified for this family in this release.
Demonstrations
- 2023: Dynamics of 3D spin glasses on thousands of qubits, in a regime the authors describe as intractable to simulate classically, with critical exponents that distinguish quantum annealing from Monte Carlo dynamics. (A. D. King et al. 2023)
Hardware platforms that fit
- Quantum annealing: Dedicated annealers: the King et al. (2023) experiment used a 5000-qubit programmable spin glass, and the infrastructure catalogue lists annealers at JUNIQ, CINECA and EuroQCS-Spain.
What you need to run it
- Classical simulation
- Simulated annealing and other classical heuristics run the same problem formulation on any computer and are the baseline to beat.
- Noisy hardware (NISQ)
- Not applicable for this family.
- Fault-tolerant machine
- Not applicable for this family.
- Annealer or analogue simulator
- An annealer with enough qubits and couplings for the problem graph after embedding; problems are sent as Ising or QUBO models through the provider’s cloud interface.
Calculate the memory of a simulation
Where to run it in Europe
Quantum annealing
- EuroQCS-Spain (Spain; Inaugurated, per the EuroHPC JU): Superconducting annealing; analogue quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones EuroQCS-Spain
- JUNIQ (Germany; In operation, per the source): Vendor-neutral user platform with quantum computing systems at different maturity levels and software emulators; open for applications: JUPSI, a D-Wave Advantage2 quantum annealer. Access: JUNIQ access, service and support.
- CINECA Quantum Computing as a Service (Italy; In operation, per the source): Cloud time on a D-Wave Advantage quantum annealer (more than 5,000 qubits; 75 hours a year) and quantum emulators on CINECA supercomputers. Access: CINECA Quantum Computing as a Service.
The full infrastructure catalogue · The infrastructure deployment tracker
Software
Other open-source frameworks
- D-Wave Ocean SDK (D-Wave (Canada); non-European)
A listing is not an endorsement; check each tool for the features you need.
Limitations and open questions
- The run time needed depends on the smallest energy gap, which is generally unknown (Farhi et al. 2000).
- Reported business cases compare with classical methods their authors chose; see each use case for what its source says.
In the Quantum Algorithm Zoo
- Adiabatic Algorithms (Quantum Algorithm Zoo, external site): Optimization, Numerics, and Machine Learning; speedup as the Zoo states it: A plausible superpolynomial example is cited
Index: the Quantum Algorithm Zoo by Stephen P. Jordan, last updated 2026-09-10, checked 2026-10-23. The portal links to it and copies no description from it. Browse the full Quantum Algorithm Zoo (external site)
Named in European procurements
- Used in: EuroHPC procurement EuroQCS-Spain (Required in the benchmark suite (scored under the award criteria); Optional, at the choice of the tenderer)
As the tender documents state; how a benchmark is weighted against others is described in each procurement.
Sources
- E. Farhi, J. Goldstone, S. Gutmann, M. Sipser (2000). Quantum Computation by Adiabatic Evolution. arXiv:quant-ph/0001106 (2000). Read: abstract page, retrieved 2026-10-23.
- A. D. King et al. (2023). Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature (2023), DOI 10.1038/s41586-023-05867-2; arXiv:2207.13800. Read: abstract page, retrieved 2026-10-23.