Bioinformatics Approach to Cancer Prediction using Quantum Clustering Algorithm for Behavioral Similarity in Gene Expression

Summary

This protocol aims to cluster gene expression data for cancer classification using a Hybrid Quantum K-Means algorithm that automatically detects the optimal number of clusters and separates them efficiently, advancing bioinformatics applications on Noisy Intermediate-Scale Quantum ( NISQ) devices.

Abstract

This study introduces a Hybrid Quantum K-Means Clustering Algorithm with automatic cluster detection for classifying cancerous and non-cancerous gene expression data. The method employs Quantum Multi-Feature Mapping for state encoding, Swap Test-based quantum distance estimation, and Quantum Gradient-Based Optimization to dynamically identify the optimal number of clusters by minimizing intra-cluster variance. Initial centroids are selected through a probability-proportional distance strategy, improving stability and accuracy. Applied to breast cancer datasets, the approach surpasses the existing quantum K-Means algorithm, achieving a Silhouette Score of 0.641 (compared to 0.601), a Calinski-Harabasz Index of 766.57 (compared to 617.65), and a Davies-Bouldin Index of 0.659 (compared to 0.704). These results indicate superior cluster compactness and separation. Although the proposed algorithm exhibits slightly higher time complexity O (N×K_max×M_obs) due to iterative optimization, it significantly outperforms predefined-K quantum K-Means in clustering accuracy, error reduction, and practical feasibility. Its efficiency in handling high-dimensional data and resilience to quantum noise highlights its potential for real-world bioinformatics applications, particularly in cancer classification using gene expression profiles.

Introduction

In biomedical engineering, bioinformatics, statistics, social sciences, and economics, clustering is a fundamental technique for organizing data into meaningful homogeneous groups. For example, topological data analysis (TDA) has been applied to cancer gene expression datasets to reveal structural patterns in high-dimensional spaces¹, Clustering organizes data such that objects with high similarity are placed within the same cluster, while dissimilar objects are assigned to different clusters. This falls under unsupervised learning and does not require labeled training data.

Over the past several decades, numerous cl....

Protocol

1. Quantum Feature Mapping

Encoding classical data points into quantum states is achieved by mapping them into a quantum Hilbert space, which can be efficiently accessed and manipulated by a quantum computer¹⁶˒^17,19. This process employs a nonlinear quantum feature map that embeds classical data into the Hilbert space (Figure 1). A fixed quantum circuit feature map transforms the input data points into quantum states¹⁷, while variational circuits enable machine learning tasks by adapting t....

Results

A good cluster will depend upon various no of factors like, separation distance between clusters, within cluster distance, variance ratio criterion etc. So, Clustering performance was evaluated using three standard indices: the Silhouette Score, the Calinski-Harabasz Index (CH Index), and the Davies-Bouldin Index (DB Index). The Silhouette Score measures separation between clusters as

Discussion

This study proposes a novel Hybrid Quantum K-Means Clustering Algorithm with Optimal Cluster Detection, specifically designed to classify cancerous and non-cancerous samples using high-dimensional gene expression data. The approach integrates Quantum Multi-Feature Mapping, Swap Test-based quantum distance estimation, and Quantum Gradient-Based Optimization to dynamically determine the optimal number of clusters. Unlike traditional K-Means algorithms, which require a predefined number of cluster.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Apple MacBook Pro (M1 chip)	Apple Inc.	-	8?core CPU / 8?core GPU, 16?GB unified memory — used for local simulation
Breast Cancer Gene Expression Dataset	Kaggle	-	Dataset with 569 samples, 32 features (reduced via PCA in study)
macOS Monterey (Operating System)	Apple Inc.	12.6.9	Runtime environment used on local machine
math (Python standard library)	Python Software Foundation	built-in	Basic mathematical functions
Matplotlib	Matplotlib community	3.8.4	Plotting and visualization
NoiseModel, QuantumError, ReadoutError (Qiskit Aer)	IBM / Qiskit project	part of Aer 0.13.3	Used to simulate realistic quantum noise
NumPy	NumPy developers	1.26.4	Numerical operations and array manipulation
pandas	pandas development team	2.2.2	Data handling, I/O, tabular operations
Python	Python Software Foundation	3.10.12	Programming language, used in Jupyter / IPython environment
Qiskit Aer	IBM / Qiskit project	0.13.3	Simulator backend, with noise modeling and execution
Qiskit IBM Runtime – Session, SamplerV2	IBM / Qiskit project	0.41.1	Execution framework for circuits in simulator
Qiskit Terra	IBM / Qiskit project	0.45.0	Quantum framework for circuit construction and transpilation
scikit-learn	scikit-learn developers	1.4.2	PCA, clustering metrics, data preprocessing