Moons Dataset

Medium

Two interleaving half circles for non-linear classification

Dataset Overview

Key characteristics and specifications

Samples

300

Features

2 (X, Y coordinates)

Classes

2 (Binary)

Difficulty

Medium

The Moons dataset consists of two interleaving half circles in a 2D space. It's a classic synthetic dataset for testing non-linear classifiers. The linearly inseparable nature of this data makes it an excellent benchmark for quantum machine learning algorithms that can exploit quantum superposition to learn non-linear decision boundaries.

Dataset Visualization

Moons dataset showing two interleaving half circles

Quantum Circuit Design

VQC architecture for non-linear separation

Feature Map Layer

Data encoding into quantum state using rotation gates parametrized by input features

Feature encoding gates:

Applied to each qubit in the circuit

Variational Ansatz

Trainable quantum circuit structure

Two-Layer Ansatz

Consists of parametrized rotation gates followed by entangling layers to capture non-linear patterns

where

Total parameters: 2 × n_qubits

Decision Boundary Analysis

Quantum advantage in non-linear separation

The Moons dataset cannot be linearly separated in the original 2D space. A quantum classifier can project the data into a higher-dimensional Hilbert space where linear separation becomes possible.

Kernel function:

Effective dimensionality: