QML Binary Classifier

Build a complete variational quantum classifier for a 2-class dataset.

QML Binary Classifier

In this challenge, you'll build a complete variational quantum classifier that distinguishes between two data classes using a trainable quantum circuit.

The Task

Classify 2D data points:

•Class A: points near [0.3, 0.3] -- label 0 (output P(0) close to 1)
•Class B: points near [1.5, 1.5] -- label 1 (output P(0) close to 0)

The Circuit Architecture

A 2-qubit variational classifier:

1.Encoding layer: Ry(x0, 0), Ry(x1, 1): encode the 2D input point
2.Entanglement: CNOT(0, 1): create correlations between encoded features
3.Variational layer: $R_{y} (θ, 0)$ : the single trainable parameter
4.Measurement: Measure qubit 0: $P (∣0 ⟩)$ is the classifier output

The classifier outputs $P (∣0 ⟩)$ . For Class A (label 0), we want $P (∣0 ⟩)$ close to 1. For Class B (label 1), we want $P (∣0 ⟩)$ close to 0.

Training by Grid Search

For a single trainable parameter $θ$ , grid search over $[0, 2 π]$ in 20 steps. For each $θ$ :

1.Classify Class A point: $P_{A} = P (∣0 ⟩)$ , want $P_{A}$ high
2.Classify Class B point: $P_{B} = P (∣0 ⟩)$ , want $P_{B}$ low
3.Compute loss: $L (θ) = (1 - P_{A})^{2} + P_{B}^{2}$
4.Find $θ$ that minimizes L

The optimal $θ$ separates the two classes in Bloch sphere geometry.

Understanding the Result

For Class A: $x_{0} = x_{1} = 0.3$ , so $R_{y} (0.3)$ rotates both qubits slightly from $∣0 ⟩$ . After CNOT and $R_{y} (θ)$ , qubit 0 measures close to $∣0 ⟩$ for the right $θ$ .

For Class B: $x_{0} = x_{1} = 1.5$ , so $R_{y} (1.5)$ rotates both qubits significantly. The entangled state after CNOT is very different from Class A, and $R_{y} (θ)$ can be tuned to make qubit 0 measure close to $∣1 ⟩$ .

The circuit can classify these two points because the encoding + entanglement creates geometrically separated states in Hilbert space.

One Parameter Can Classify Two Classes

This classifier uses only a single trainable parameter $θ$ , yet it can perfectly separate Class A from Class B. This is possible because the encoding and entanglement layers map the two data points to very different quantum states. The variational layer only needs to find the rotation angle that best aligns those states with the measurement axis. Real QML classifiers use more parameters for complex datasets, but the same principle applies: encoding creates the separation, variational layers find the alignment.

How this lesson works

A hands-on coding challenge. You write Qiskit-compatible Python in the browser editor, run it instantly via WebAssembly, watch the circuit and Bloch sphere react, and pass automatic output checks. The AI tutor Qubitus gives Socratic hints if you get stuck.

Part of: Quantum Machine Learning

Apply quantum computing to machine learning with variational circuits and optimization.

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