Quantum kernel methods for machine learning
Algorithms and benchmarks / Machine learning
Uses a quantum circuit to map data into a large feature space and estimates similarities (kernels) between data points there, for use in a classical support vector machine.
- Era
- Noisy intermediate-scale (NISQ)
- Problem class
- Machine learning
- Speedup
- Not established for practical data sets.
How it works
Each data point sets the angles of a feature-map circuit; the overlap of two such states, estimated on the quantum computer, gives the kernel entry; training happens classically.
Typical use cases
- Classification and forecasting tasks in finance, energy and industry pilots.
Documented use cases on related problems
From the use case directory; the sources of these cases may use other methods than this one.
Resource estimates
No resource estimate with stated assumptions was verified for this family in this release.
Demonstrations
- 2019: Quantum kernel estimation and a quantum variational classifier on a superconducting processor. (V. Havlíček et al. 2019)
Hardware platforms that fit
- Superconducting qubits: A quantum kernel estimator and a variational classifier were implemented on a superconducting processor (Havlíček et al. 2019).
What you need to run it
- Classical simulation
- A state-vector simulator holds 2^n complex amplitudes, so memory doubles with every qubit: about 30 qubits fit in 16 GiB at double precision. Circuits with little entanglement can go further with tensor-network methods. See the guide for the calculator.
- Noisy hardware (NISQ)
- Tens of qubits and very many circuit runs (one per pair of data points), so throughput (see CLOPS) matters.
- Fault-tolerant machine
- Not applicable for this family.
- Annealer or analogue simulator
- Not applicable for this family.
Calculate the memory of a simulation
Where to run it in Europe
Superconducting qubits
- VLQ (Czechia; Inaugurated, per the EuroHPC JU): Superconducting; digital quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones VLQ
- Euro-Q-Exa (Germany; Inaugurated, per the EuroHPC JU): Superconducting; digital quantum computer. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones Euro-Q-Exa
- 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
- Quantum Inspire (Netherlands; In operation, per the source): Online platform with superconducting transmon QPUs, a neutral-atom emulator and simulators; a Spin-2+ electron spin QPU is listed as archived. Access: Quantum Inspire registration.
- LRZ Quantum Integration Centre (QIC) (Germany; In operation, per the source): Superconducting systems from IQM (54 qubits, up to 150 in future), a 20-qubit AQT ion-trap system, and a neutral-atom system being developed by planqc (MAQCS project). Access: LRZ quantum computing consulting.
- Finnish Quantum-Computing Infrastructure (FiQCI) (Finland; In operation, per the source): Hybrid HPC and quantum computing platform: VTT Q50 (53 qubits) and Aalto Q20 (20 qubits), superconducting systems made by IQM, used through the LUMI supercomputer environment. Access: FiQCI calls for academic projects.
- Quantum Spain quantum computer at BSC-CNS (Spain; In operation, per the source): Superconducting; digital quantum computer with a 35-qubit processor, integrated into the MareNostrum 5 supercomputer. Access: Spanish Supercomputing Network (RES) quantum access. Deployment milestones Quantum Spain quantum computer at BSC-CNS
The full infrastructure catalogue · The infrastructure deployment tracker
Software
European tools in the software directory
Other open-source frameworks
A listing is not an endorsement; check each tool for the features you need.
Limitations and open questions
- Kernel values are estimated from many shots, so sampling noise limits their precision.
- Classical methods are strong baselines; claims of advantage need careful comparison.
In the Quantum Algorithm Zoo
- Machine Learning (Quantum Algorithm Zoo, external site): Optimization, Numerics, and Machine Learning; speedup as the Zoo states it: Varies
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
None of the procurement documents read for this release names it.
Sources
- V. Havlíček et al. (2019). Supervised learning with quantum enhanced feature spaces. Nature 567, 209 (2019); arXiv:1804.11326. Read: abstract page, retrieved 2026-10-23.