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.
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.
Clustering remains a cornerstone of unsupervised learning, yet classical algorithms often struggle with the inherent complexities of modern datasets, such as high dimensionality, non-linear separability, and significant noise. This paper introduces the Hybrid Quantum-Classical Clustering Algorithm (HQCA), a novel framework that leverages the power of quantum computation and the robustness of classical machine learning to overcome these limitations. HQCA integrates a quantum kernel estimation phase, utilizing a parameterized quantum circuit to project data into a high-dimensional Hilbert space, thereby enhancing cluster separability where classical kernels fail. Furthermore, it employs a quantum-enhanced optimization routine, based on the Quantum Approximate Optimization Algorithm (QAOA), to determine optimal cluster centroids, thereby mitigating the common pitfall of local minima encountered by algorithms like K-Means. The algorithm also incorporates a quantum-inspired gap statistic to autonomously determine the optimal number of clusters. We rigorously evaluate HQCA against state-of-the-art classical clustering methods, including K-Means, DBSCAN, and Spectral Clustering, on multiple real-world benchmark datasets from the UCI repository, such as Iris, Wine, and a high-dimensional image dataset (Fashion-MNIST). Our results demonstrate that HQCA consistently achieves superior performance across multiple evaluation metrics, including Purity, Silhouette Score, and Adjusted Rand Index (ARI), particularly excelling in scenarios involving complex, non-linear data manifolds. The proposed hybrid paradigm not only signifies a substantial leap in clustering accuracy and robustness but also provides a scalable pathway for leveraging current Noisy Intermediate-Scale Quantum (NISQ) devices in practical data analytics workflows, marking a critical step toward potential quantum advantage in unsupervised learning. We emphasize that the demonstrated advantage is algorithmic and representational, not an asymptotic runtime advantage.
Quantum machine learning promises computational advantages for certain tasks, yet rigorous empirical evaluation of quantum clustering algorithms against classical baselines remains limited. This paper presents a comprehensive implementation and comparative analysis of two quantum K-means clustering algorithms—SWAP Test-based and Quantum Fidelity-based—against classical K-means on benchmark datasets. Both quantum approaches employ amplitude encoding to map classical data into quantum state amplitudes and use quantum-native distance metrics derived from inner products in Hilbert space. All three methods are evaluated on the ENB2012 energy efficiency dataset (768 samples, 8 features) and a synthetically expanded high-dimensional dataset (4,998 samples, 16 features), measuring silhouette score, inertia, and wall-clock execution time across cluster counts k ∈ {2, . . . , 7}. The experiments, conducted on Qiskit’s AerSimulator and Statevector backends, show that classical K-means achieves substantially higher silhouette scores (0.391 vs. 0.031 on the original dataset) and orders-of-magnitude faster execution. A rigorous analysis attributes these results to three factors: (i) the information loss inherent in amplitude encoding normalization, (ii) the geometric mismatch between Euclidean and Hilbert-space distance metrics, and (iii) the absence of quantum parallelism in classical simulation. The implications for quantum advantage in unsupervised learning are discussed and concrete requirements for near-term quantum hardware to achieve competitive clustering performance are outlined.
The recent rise in the number of data-intensive applications has revealed some inherent limitations of traditional machine learning, such as high training costs, slow convergence rates, and the uncapable of scalability of traditional machine learning in high-dimensional spaces. Bottlenecks are caused by the iterative optimization procedure, kernel evaluations, and similarity computations that are not efficiently supported by traditional hardware. Although recent advances in quantum computing, such as the Variational Quantum Algorithm, quantum kernels, and parameterized quantum circuits, hold promise for acceleration, the application of quantum speedup is presently hindered by noisy intermediate-scale quantum computing. This research provides a hybrid quantum-classical acceleration method that integrates quantum methods with selected computationally intensive components of classical machine learning systems rather than attempting to entirely replace them. Carried out a comprehensive analysis of the performance of well-known algorithms like Support Vector Machines, k-means clustering, and gradient-based neural networks in classical and quantum-assisted hybrid scenarios. The quantum resources are greatly beneficial for particular sub-tasks such as optimization, approximation of similarity, and exploration of the feature space, with the remaining learning process performed classically. Our analysis reveals that hybrid methods can offer a tangible acceleration and improved convergence behaviour in particular scenarios without sacrificing accuracy. Moreover, the analysis investigates the trade-offs associated with the utilization of quantum resources, robustness to noise, and orchestration costs.
The recent rise in the number of data-intensive applications has revealed some inherent limitations of traditional machine learning, such as high training costs, slow convergence rates, and the uncapable of scalability of traditional machine learning in high-dimensional spaces. Bottlenecks are caused by the iterative optimization procedure, kernel evaluations, and similarity computations that are not efficiently supported by traditional hardware. Although recent advances in quantum computing, such as the Variational Quantum Algorithm, quantum kernels, and parameterized quantum circuits, hold promise for acceleration, the application of quantum speedup is presently hindered by noisy intermediate-scale quantum computing. This research provides a hybrid quantum-classical acceleration method that integrates quantum methods with selected computationally intensive components of classical machine learning systems rather than attempting to entirely replace them. Carried out a comprehensive analysis of the performance of well-known algorithms like Support Vector Machines, k-means clustering, and gradient-based neural networks in classical and quantum-assisted hybrid scenarios. The quantum resources are greatly beneficial for particular sub-tasks such as optimization, approximation of similarity, and exploration of the feature space, with the remaining learning process performed classically. Our analysis reveals that hybrid methods can offer a tangible acceleration and improved convergence behaviour in particular scenarios without sacrificing accuracy. Moreover, the analysis investigates the trade-offs associated with the utilization of quantum resources, robustness to noise, and orchestration costs.
Hybrid quantum-classical computing offers a promising pathway to harness quantum advantages while mitigating the hardware limitations of noisy intermediate-scale quantum (NISQ) devices. This work proposes a modular hybrid architecture that combines classical preprocessing, quantum-enhanced feature mapping through parameterized quantum circuits (PQCs), and adaptive classical optimization. The framework is designed to improve robustness and generalization of machine learning models in noisy environments, addressing critical issues such as overfitting, noise sensitivity, and hardware-induced errors. Experimental evaluations were conducted on benchmark datasets, including Iris, reduced-dimension MNIST, synthetic noisy XOR, Wine Quality, and Breast Cancer Wisconsin. The proposed model was tested under multiple noise models, such as Gaussian, salt-and-pepper, Poisson, and quantum-specific errors (bit-flip, phase-flip, and depolarizing), using 5-fold cross-validation and repeated trials for statistical rigor. Key performance metrics included Classification Accuracy (CA), Robustness Index (RI), and Training Stability (TS), with results reported as mean ± standard deviation and supported by paired t-tests (p < 0.05). Results demonstrate that the hybrid model consistently outperforms classical support vector machines (SVM) and standalone variational quantum classifiers (VQC) in noisy conditions, achieving smaller accuracy degradation and higher stability. The combination of quantum- enhanced feature mapping, optimizer synergy, and modular design is shown to be central to its resilience.