Quantum K-Means Clustering

A genuine quantum computing implementation of K-Means clustering using SWAP test and quantum fidelity-based distance metrics.

Paper

The accompanying research paper is archived on Zenodo under the CC BY-NC 4.0 license:

Sricharan, "Comparative Analysis of Classical and Quantum K-Means Clustering: SWAP Test and Fidelity-Based Approaches on Benchmark Datasets," Feb 2026. DOI: 10.5281/zenodo.18802705

Overview

This project implements authentic quantum K-Means clustering algorithms that leverage fundamental quantum computing principles:

• SWAP Test - Uses quantum interference to compute inner products between quantum states
• Quantum Fidelity - Measures similarity in Hilbert space via statevector simulation
• Amplitude Encoding - Maps classical data to quantum state amplitudes

Unlike pseudo-quantum implementations, this project uses real quantum circuits executed on Qiskit's quantum simulators.

Key Features

Feature	Description
Genuine Quantum Circuits	Real SWAP test implementation with controlled-SWAP operations
Multiple Distance Metrics	Quantum fidelity and SWAP-based inner product estimation
Amplitude Encoding	Efficient classical-to-quantum data mapping
Comparative Analysis	Side-by-side classical vs quantum performance evaluation
Scalable Design	Works with datasets from hundreds to thousands of samples

Quantum Algorithms Implemented

SWAP Test

The SWAP test computes the quantum inner product |⟨ψ₁|ψ₂⟩|² using quantum interference:

P(ancilla=0) = (1 + |⟨ψ₁|ψ₂⟩|²) / 2

Circuit Structure:

|0⟩ ──H──●──H──M
         │
|ψ₁⟩ ────×────
         │
|ψ₂⟩ ────×────

Quantum Fidelity

Direct computation of state fidelity F = |⟨ψ₁|ψ₂⟩|² with distance:

d = √(2(1-F))

Datasets

Dataset	Samples	Features	Description
Original (ENB2012)	768	10	Energy efficiency benchmark (X1-X8 + Y1-Y2)
Quantum-Optimized	4,998	16	High-dimensional expanded dataset

Quick Start

Prerequisites

pip install numpy pandas scikit-learn matplotlib qiskit qiskit-aer

Run Analysis

cd code
python comprehensive_quantum_classical_analysis.py

Generate Quantum Dataset

python create_quantum_optimized_dataset.py

Project Structure

quantum-kmeans/
├── code/
│   ├── comprehensive_quantum_classical_analysis.py  # Main analysis script
│   └── create_quantum_optimized_dataset.py          # Dataset generator
├── data/
│   ├── ENB2012_data.csv                             # Original dataset
│   └── quantum_optimized_ENB_data.csv               # Expanded dataset
├── output/
│   ├── quantum_classical_analysis_report_*.txt      # Analysis reports
│   └── quantum_classical_comparison_*.png           # Visualization plots
├── README.md
├── LICENSE
└── Report.md                                        # Detailed research report

Sample Results

Classical vs Quantum Performance

Dataset	Method	Best k	Silhouette Score
Original (768×8)	Classical K-Means	2	0.391
Original (768×8)	Quantum SWAP Test	2	varies
Original (768×8)	Quantum Fidelity	2	varies
Expanded (4998×16)	Classical K-Means	2	0.149
Expanded (4998×16)	Quantum SWAP Test	2	varies
Expanded (4998×16)	Quantum Fidelity	4	varies

Technical Details

Quantum Encoding

Classical data points are encoded into quantum states using amplitude encoding:

|ψ⟩ = Σᵢ αᵢ|i⟩  where αᵢ = normalized_feature_i

This allows encoding N features using only log₂(N) qubits.

Distance Computation

Quantum distance between encoded states:

quantum_distance = √(2(1 - |⟨ψ₁|ψ₂⟩|))

K-Means++ Initialization

Uses intelligent centroid initialization for better convergence.

Limitations

• Simulation Overhead: Quantum circuits run on simulators, not actual quantum hardware
• Scalability: SWAP test requires O(n×k) circuit executions per iteration
• Noise: Statistical estimation introduces measurement uncertainty

Future Work

• Implementation on IBM Quantum hardware
• Variational quantum eigensolver (VQE) integration
• Quantum error correction
• Hybrid classical-quantum optimization

License

Copyright © 2026 Sricharan Suresh (github.com/verycareful)

This project is licensed under the Apache License 2.0. You may use, modify, and distribute this software in accordance with Apache 2.0 terms.

See the LICENSE file for full text and NOTICE for attribution information.

References

1. Quantum K-means algorithm - Lloyd, S., Mohseni, M., & Rebentrost, P. (2013)
2. SWAP test for quantum states - Buhrman, H., et al. (2001)
3. Qiskit Documentation - IBM Quantum

Author

Sricharan

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Exploring the intersection of quantum computing and machine learning