ExperimentsExperiment 14 · Quantum AI

Quantum Machine Learning

Train a 2-qubit variational classifier with the parameter-shift rule.

1. Learn
2. Watch
3. Interact
4. Predict
5. Run
6. Observe
7. Record
8. Answer
9. Research

① What is the problem?

Can a quantum circuit learn to classify data?

② How does a classical computer approach it?

A classical model (e.g. logistic regression) adjusts weights to reduce error.

③ How does the quantum approach differ?

A parameterized circuit encodes data as rotation angles; trainable angles are adjusted so the measured probability predicts the class.

Classical data ↓
Encoding ↓
Quantum circuit ↓
Measurement ↓
Prediction

Decision map (every pixel = one circuit simulation)

● class 0 · ▲ class 1 · red outline = misclassified. Tap the map to test a new point.

Tip: select any gate to learn what it does.

Epoch

Loss (MSE)

0.260

Accuracy

56%

weights w = [0.13, -0.28, -0.03, -0.26]

What is quantum machine learning?

Classical data is encoded into rotation angles, a parameterized quantum circuit processes it, and measurement probabilities become predictions. The angles are trained by gradient descent using the parameter-shift rule. No practical quantum advantage is claimed: this 16-point problem is trivial for classical ML — it shows how the pipeline works.

④ What is happening mathematically?

Prediction f(x;w) = P(q₁=1). Gradient by parameter shift: ∂f/∂w = [f(w+π/2) − f(w−π/2)]/2.

⑤ What does the simulation show?

Data, the circuit, the decision map and the loss curve — every value from the statevector simulator.

⑥ What did we learn?

QML is a young research field. Small circuits can learn simple patterns; practical quantum advantage has not been demonstrated for problems like this.

⑦ What can you experiment with?

Switch datasets and retrain. How many epochs until accuracy is 100%?

📓 Record: my lab notebook

Write your observations. Notes are saved only in this browser.