Algorithm Zoo · Machine learning
Quantum Kernel Methods
Also known as: Quantum SVM, Quantum feature maps
First described: Havlíček et al.; Schuld, Killoran, 2018
The problem
Classify data using a kernel computed by a quantum feature map.
Map xi → |φ(xi)⟩ with a parameterized quantum circuit; estimate kernel K(xi, xj) = |⟨φ(xi)|φ(xj)⟩|² via overlap measurement; train an SVM with that kernel.
Best classical
RBF kernels, polynomial kernels — extremely well understood and strong.
Quantum complexity
O(D) shots per kernel entry for D-bit precision; O(N²) entries for N data points.
Our verdict
Kernels are a clean way to think about QML but they don't get you out of the QML problem. The Liu-Arunachalam-Temme construction shows a separation exists in principle on a discrete-log-based dataset; no comparable result is known for real datasets. Treat as research, not as production ML.
When to use it
- Research into feature-map design and expressibility/trainability tradeoffs.
- Synthetic problems with structure matched to the quantum feature map (Liu, Arunachalam, Temme 2021 has a contrived example with provable separation).
When not to use it
- Real datasets. Every published benchmark on MNIST-like data has had a classical kernel that matches or beats the quantum one.
- When the kernel cost dominates the win — shot noise + barren-plateau-style flatness kills scaling.
Classical baseline
scikit-learn's RBF kernel SVM trains in minutes on standard benchmarks with accuracy that matches all published quantum-kernel results. Schuld 2021 commentary: 'quantum kernels are kernels' — no exponential separation has been demonstrated on natural data.
Hardware cost
N² overlap circuits — quickly becomes the dominant cost. For 1,000 training points: 500,000 quantum kernel evaluations.
Key papers
- Supervised learning with quantum-enhanced feature spaces ↗
Havlíček, Córcoles, Temme, Harrow, Kandala, Chow, Gambetta · 2019 · Nature
- A rigorous and robust quantum speed-up in supervised machine learning ↗
Liu, Arunachalam, Temme · 2021 · Nature Physics
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Last verified: 2026-05-24