A basic use case of quantum computing for machine learning, made for my Quantum Machine Learning course at SRM IST: a support vector machine whose kernel is computed by a two-qubit circuit.
Site and live demo: https://zanyanbu.github.io/quantum-kernel-classifier/
Slides: Quantum-Kernel-Classifier.pptx · PDF
Two rings of points cannot be separated by a straight line. A support vector machine only needs to know how similar each pair of points is, so the similarity measure (the kernel) can be swapped. Here it is measured by a quantum circuit:
- Encode. A ZZ feature map (Hadamard, phase and ZZ gates) turns a point's two features into a two-qubit state.
- Compare. Encode one point, undo the encoding of another, and measure. The probability of reading
00is the kernel value for that pair. - Train. Fill the kernel matrix and pass it to an ordinary support vector machine.
120 points on two rings, 80 for training and 40 for testing.
| Kernel | Test accuracy |
|---|---|
| Linear (classical) | 60.0% |
| Quantum, 1 layer | 95.0% |
| Quantum, 2 layers | 97.5% |
| RBF (classical) | 100.0% |
Reproduce these numbers with:
node experiment.js- No quantum advantage. The classical RBF kernel does as well or better, and two qubits are trivial to simulate.
- No noise. The circuit is simulated exactly. Real hardware estimates each kernel value from repeated runs.
- Cost.
ntraining points needn(n−1)/2circuits.
| File | What it is |
|---|---|
qkernel.js |
Datasets, the two-qubit feature map, the quantum kernel and a small SVM solver. Runs in the browser and in Node, with no dependencies. |
experiment.js |
Prints the accuracy table above. |
index.html, style.css, app.js |
The site and the live demo. |
Quantum-Kernel-Classifier.pptx |
The ten slides. |
assets/ |
Pictures used by the slides and the site. |
- Havlíček et al., "Supervised learning with quantum-enhanced feature spaces", Nature 567 (2019).
- Schuld and Killoran, "Quantum machine learning in feature Hilbert spaces", Physical Review Letters 122 (2019).
MIT