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×Kmax×Mobs) 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.
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×Kmax×Mobs) 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.
Clustering is one of the most fundamental tasks in machine learning, and the k-means clustering algorithm is perhaps one of the most widely used clustering algorithms. However, it suffers from several limitations, such as sensitivity to centroid initialization, difficulty capturing non-linear structure, and poor performance in high-dimensional spaces. Recent work has proposed improved initialization strategies and quantum-assisted distance computation, but the similarity metric itself has largely remained classical. In this study, we propose a quantum-enhanced variant of k-means that replaces the Euclidean distance with a quantum kernel derived from the inner product between feature-mapped quantum states. Using the Iris dataset, we use multiple quantum feature maps, including entangled SU2 and ZZ circuits, to embed classical data into a higher-dimensional Hilbert space where cluster structures become more separable. We will also be testing using another dataset, namely the breast cancer dataset. Similarity between data points is computed through the inner product between two states. Our results show that this approach achieves improved clustering stability and competitive accuracy compared to the classical algorithm, with the SU2 feature map yielding an accuracy of 88.6 % on the Iris dataset and 91.0 % on the breast cancer dataset, despite operating on NISQ-feasible shallow circuits. These findings suggest that quantum kernels provide a richer similarity landscape than traditional distance metrics, offering a promising path toward more robust unsupervised learning in the NISQ era.
Recently, the volume of the generated data has increased significantly, leading to the need for computational techniques capable of handling such data efficiently. As a result, many quantum algorithms have been developed, and the domain of quantum machine learning (QML) has become more extensive. Traditional k-means algorithms for quantum computers usually make use of deep or shallow quantum circuits, resulting in sub-optimal clustering results. In our work, we introduce two types of quantum-inspired k-means algorithm: (1) the quantum subtraction operation and (2) the rotational-difference dissimilarity measure. Our second framework measures the dissimilarity using a quantum rotation-based dissimilarity circuit, which encodes the relative difference of the states. We employ a Hadamard-test-based circuit design, as well as an alternative technique that is not used in other quantum dissimilarities like the swap test. The introduced algorithms are evaluated on six different datasets—Iris, Wine, Breast Cancer Wisconsin, Blobs, Moons, and the noisier Iris dataset. Evaluation involves clustering validity metrics, as well as the classic classification performance metrics. The findings show that the rotational-based dissimilarity metric allows us to obtain clustering results comparable with the results obtained by the classical counterpart, thus showing the feasibility of the introduced distance calculation technique.
A quantified RNA transcriptome is of particular interest in biomedical research as it can be for cancer diagnosis. Quantum algorithms can give exponential performance gains over their classical counterparts. In this paper, we implement a quantum clustering technique to classify the cells into different cancer types. To verify our implementation, we test it using the standard ‘gene expression cancer RNA-Seq’ dataset. The experimental results show that our algorithm achieves high accuracy of 94.8% (on average) in classifying the different types of cancer.
This study investigates hybrid quantum-classical K-Means algorithms for clustering heart disease patient data. Using quantum swap-test circuits for distance calculation, 2 approaches were tested on both noisy and ideal quantum simulators. A real-world dataset of over 1,000 records was preprocessed using standard techniques, including normalization, outlier removal, and dimensionality reduction. The results show that both quantum methods achieve accuracy up to 0.83 and F1-scores comparable to the classical K-Means baseline (0.82 - 0.83), even when executed on quantum simulators with real-device noise models. These findings highlight the practical potential of quantum-enhanced clustering methods. The study supports the feasibility of applying quantum-enhanced clustering in medical analytics, particularly for early-stage heart disease detection and patient risk stratification. HIGHLIGHTS This paper introduces a hybrid quantum–classical K-Means clustering framework for analyzing heart disease data. Two quantum circuits for distance calculation are designed and evaluated on a real-world dataset using both ideal quantum simulators and noisy quantum hardware (e.g., IBM’s ibm_brisbane). The quantum clustering algorithms demonstrate performance comparable to classical K-Means and traditional models such as XGBoost. Future work will focus on circuit optimization, scalable encoding strategies, and validation on larger datasets using real quantum devices. GRAPHICAL ABSTRACT
Cancer classification based on gene expression increases early diagnosis and recovery, but high-dimensional genes with a small number of samples are a major challenge. This work introduces a new hybrid quantum-kernel support vector machine (QKSVM) combined with a Binary Harris hawk optimization (BHHO)-based gene selection for cancer classification on a quantum simulator. This study aims to improve the microarray cancer prediction performance with the quantum kernel estimation based on the informative genes by BHHO. The feature selection is a critical step in large-dimensional features, and BHHO is used to select important features. The BHHO mimics the behavior of the cooperative action of Harris hawks in nature. The principal component analysis (PCA) is applied to reduce the selected genes to match the qubit numbers. After which, the quantum computer is used to estimate the kernel with the training data of the reduced genes and generate the quantum kernel matrix. Moreover, the classical computer is used to draw the support vectors based on the quantum kernel matrix. Also, the prediction stage is performed with the classical device. Finally, the proposed approach is applied to colon and breast microarray datasets and evaluated with all genes and the selected genes by BHHO. The proposed approach (QKSVM{PCA{BHHO) is found to enhance the overall performance with two datasets. Also, the proposed approach is evaluated with different quantum feature maps (kernels) and classical kernel (RBF).
The quantum-inspired neural architecture has a transformative capability for high-efficiency signal processing in the field of bioinformatics. Incorporating the principles of quantum computing in combination with classic neural networks, hybrid models use quantum superposition, entanglement, and parallelism to tackle difficult problems in biological data. As an example, the Quantum Spiking Neural Network (QSNN) combined with Quantum Long Short-Term Memory (QLSTM) modules can perform dynamic pattern recognition on genomic sequences and protein interaction predictions, which outperforms data efficiency in classical deep learning models. Quantum kernel methods also provide additional improvements in semantic classification tasks where quantum similarity is calculated between the biological data points, as can be seen in the analysis of gene expression with Quantum Kernel Support Vector Machines (QK-SVM). Areas of application include the transcriptomics classification of cancer using quantum k-means clustering, the optimization of gene regulatory networks, and fast drug discovery by means of quantum-enhanced literature mining. Such architectures both lower computational complexity and accelerate convergence rates - quantum-inspired backpropagation mechanisms, as an example, optimize weight updates 30% faster than classical counterparts in molecular dynamics simulations. The convergence of quantum-inspired algorithms and bioinformatics promises to not only solve the scalability problem in multi-omics data but also explore new methods of real-time adaptive learning in noisy biological settings