The classical K-means clustering algorithm is widely used in various fields due to its simple implementation and efficient computation, but the classical K-means clustering algorithm relies on the random selection of the initial center of mass, which is prone to fall into the deadlock of local optimality. In order to break through this limitation, the quantum K-means clustering algorithm is introduced, which is able to explore multiple potential clustering center combinations at the same time through the parallelism of quantum computation, so as to have a greater probability of converging to the globally optimal solution. Quantum K-means clustering algorithms typically employ fidelity as a similarity measure between quantum states, and similarity is assessed by calculating the probability of overlap between quantum states. However, the fidelity only quantizes the pure state information of the quantum states and ignores the classical statistical features of the data itself, which may lead to unreasonable clustering boundaries in mixed state or noise interference scenarios. In response to the above problems, this paper proposes an improved quantum-classical hybrid similarity metric, whose core idea is to incorporate the dual constraints of quantum information and classical features.
The classical K-means clustering algorithm is widely used in various fields due to its simple implementation and efficient computation, but the classical K-means clustering algorithm relies on the random selection of the initial center of mass, which is prone to fall into the deadlock of local optimality. In order to break through this limitation, the quantum K-means clustering algorithm is introduced, which is able to explore multiple potential clustering center combinations at the same time through the parallelism of quantum computation, so as to have a greater probability of converging to the globally optimal solution. Quantum K-means clustering algorithms typically employ fidelity as a similarity measure between quantum states, and similarity is assessed by calculating the probability of overlap between quantum states. However, the fidelity only quantizes the pure state information of the quantum states and ignores the classical statistical features of the data itself, which may lead to unreasonable clustering boundaries in mixed state or noise interference scenarios. In response to the above problems, this paper proposes an improved quantum-classical hybrid similarity metric, whose core idea is to incorporate the dual constraints of quantum information and classical features.
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.
Abstract Quantum state clustering provides a powerful tool for quantum information processing. This paper focuses on the classification of single-qubit pure and mixed states via clustering algorithms, and discovers that the classical K -means algorithm has two limitations in clustering quantum states: the Euclidean distance cannot accurately reflect the similarity between quantum states, and the centroid update based on the arithmetic mean frequently fails to yield valid quantum states. To address these issues, we propose two distance metrics for quantum states: the dynamic distance and the Bloch distance, and adopt the K -medoids method to update the centroid, ensuring that the cluster center always remains a valid quantum state, thereby designing a quantum-data-adaptive clustering algorithm. Experimental results show that the dynamic distance achieves a clustering accuracy as high as 91.4 % , but at the cost of higher computational complexity. In contrast, the Bloch distance significantly reduces computational complexity while maintaining clustering performance comparable to that of the dynamic distance, achieving a clustering accuracy of 87.4 % . This paper provides a practical method for achieving efficient and reliable clustering of single-qubit quantum states.
The Quantum K-means clustering algorithm offers the advantage of quantum parallel computing, but suffers from issues related to cluster center initialization and sensitivity to noisy data due to its similarity with the K-means clustering algorithm. To address these challenges, we propose a quantum K-means model based on an optimization framework. Specifi-cally, we use a quantum genetic algorithm with pin optimization to adjust the fitness function for the Quantum K-means clustering algorithm. The optimally adapted quantum genetic algorithm reduces the sensitivity of cluster center initialization and improves the noise robustness of the Quantum K-means clus-tering algorithm using a noise reduction self-encoder. As a result, the proposed model achieves better clustering performance even in the presence of noise. Experimental results demonstrate that our proposed quantum K-means model has fewer clustering iterations, lower probability of falling into local optima, and improved noise robustness after optimizing the clustering cen-ters. The model's effectiveness in clustering is also demon-strated experimentally.
Traditional clustering algorithms, such as k-means and DBSCAN, often face significant challenges when applied to big data. The computational complexity associated with distance calculations and nearest neighbor searches scales poorly with dataset size, limiting their effectiveness. This paper proposes a novel approach to clustering inspired by quantum measurement theory, specifically quantum-inspired nearest neighbor search. We leverage concepts from quantum mechanics, such as superposition and measurement, to design clustering algorithms that can efficiently identify clusters within high-dimensional datasets. The core idea is to treat the clustering problem as a measurement process, where candidate cluster centers are repeatedly measured against data points, and the most likely cluster centers are selected. The resulting algorithms aim to provide scalability improvements over conventional methods, particularly for datasets with a large number of features and data points. The effectiveness of the proposed algorithms is demonstrated through theoretical analysis and conceptual explanations, highlighting the potential benefits and future research directions.
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.
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.