Variational quantum neural networks
Algorithms and benchmarks / Machine learning
Parameterised quantum circuits trained like neural networks for classification, regression or generative modelling, often as one layer of a hybrid classical model.
- Era
- Noisy intermediate-scale (NISQ)
- Problem class
- Machine learning
- Speedup
- Not established.
How it works
Inputs are encoded in a circuit with trainable gates; measured outputs feed a loss function, and gradients estimated on the quantum computer or a differentiable simulator update the parameters.
Typical use cases
- Forecasting and classification in energy, finance and health 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: Variational quantum classifier on a superconducting processor. (V. Havlíček et al. 2019)
Hardware platforms that fit
- Neutral atoms: Energy demand forecasting for electric vehicle charging ran on more than 100 qubits of a neutral-atom computer (EDF, Pasqal and GENCI, on /adopt).
- Superconducting qubits: The variational classifier of Havlíček et al. (2019) ran on a superconducting processor.
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. Differentiable simulators (such as PyQTorch) train small models on GPUs.
- Noisy hardware (NISQ)
- Tens to around a hundred qubits, many shots per gradient, low-latency coupling with classical training.
- 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
Neutral atoms
- JADE (Germany; Inaugurated, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. No access route named in the catalogue. Deployment milestones JADE
- Ruby (France; Inaugurated, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. Access: EuroHPC JU call for quantum access in pilot mode. Deployment milestones Ruby
- SOL (Italy; Planned, per the EuroHPC JU): Neutral atoms; analogue/digital quantum simulator. No access route named in the catalogue. Deployment milestones SOL
- 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.
- France Hybrid HPC Quantum Initiative (HQI) platform (France; In operation, per the source): Hybrid HPC–quantum platform coupled to the Joliot-Curie supercomputer: Ruby (analogue neutral-atom system controlling 100 rubidium atoms), Lucy (12-photon photonic QPU) and Qaptiva QPU emulation. Access: GENCI eDARI resource allocation requests. Deployment milestones France Hybrid HPC Quantum Initiative (HQI) platform
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
- PennyLane (Xanadu (Canada); non-European)
A listing is not an endorsement; check each tool for the features you need.
Limitations and open questions
- Barren plateaus: gradients vanish exponentially with qubit number for many circuit families (McClean et al. 2018).
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
- J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, H. Neven (2018). Barren plateaus in quantum neural network training landscapes. Nature Communications 9, 4812 (2018); arXiv:1803.11173. Read: abstract page, retrieved 2026-10-23.
- 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.