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arXiv:2212.06691 · Theoretical Computer Science

Quantum clustering with k-Means: A hybrid approach

Alessandro Poggiali, Alessandro Berti, Anna Bernasconi, Gianna M. Del Corso, Riccardo Guidotti

Published Feb 21, 2024• 50 citations
arXivHTMLPDF

Abstract

Quantum computing, based on quantum theory, holds great promise as an advanced computational paradigm for achieving fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including machine learning. In this paper, we design, implement, and evaluate three hybrid quantum k-Means algorithms, exploiting different degrees of parallelism. Indeed, each algorithm incrementally leverages quantum parallelism to reduce the complexity of the cluster assignment step up to a constant cost. In particular, we exploit quantum phenomena to speed up the computation of distances. The core idea is that the computation of distances between records and centroids can be executed simultaneously, thus saving time, especially for big datasets. We show that our hybrid quantum k-Means algorithms are theoretically faster than the classical algorithm, while experiments suggest that it is possible to obtain comparable clustering results.

DOI
10.1016/j.tcs.2024.114466

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Quantum computing, based on quantum theory, holds great promise as an advanced computational paradigm for achieving fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including machine learning. In this paper, we design, implement, and evaluate three hybrid quantum k-Means algorithms, exploiting different degrees of parallelism. Indeed, each algorithm incrementally leverages quantum parallelism to reduce the complexity of the cluster assignment step up to a constant cost. In particular, we exploit quantum phenomena to speed up the computation of distances. The core idea is that the computation of distances between records and centroids can be executed simultaneously, thus saving time, especially for big datasets. We show that our hybrid quantum k-Means algorithms are theoretically faster than the classical algorithm, while experiments suggest that it is possible to obtain comparable clustering results.
Classical machine learning algorithms are increasingly challenged by the growing complexity of datasets, motivating the exploration of quantum computing as a potential solution. However, current literature lacks comprehensive empirical analyses directly benchmarking classical algorithms against quantum-assisted counterparts for small but high-dimensional standardized datasets. This research aims to address this gap by comparing the performance of the k-means clustering algorithm on classical and hybrid quantum-classical computing platforms. Using a small dataset, we assess computational speed, clustering accuracy, and scalability. Our findings reveal that while hybrid quantum implementations offer theoretical benefits, in practice they incur significantly higher computational overhead and reduced clustering accuracy due to current technological constraints. These insights highlight the critical need for improved quantum hardware and algorithms, guiding future research directions in quantum-enhanced machine learning.
The exponential growth of data and the increasing complexity of high-dimensional classification problems have pushed classical computing methods to their limits. Quantum computing emerges as a promising paradigm to address these challenges. This research article explores advanced quantum algorithms for big data clustering and high-dimensional classification. We investigate quantum versions of K-means, spectral clustering, and support vector machines, comparing their performance with classical counterparts. Our results demonstrate significant speedups in processing time and improvements in clustering quality for high-dimensional datasets. Additionally, we propose a novel quantum-inspired classical algorithm that bridges the gap between quantum and classical approaches. This comprehensive study provides insights into the potential of quantum computing in revolutionizing data analysis and machine learning, paving the way for future advancements in the field.
The article introduces Q-ClusterSim, a resource-efficient hybrid quantum-classical framework designed to accelerate clustering operations on large-scale and high-dimensional datasets. The proposed model combines quantum-enhanced k-means and density-based clustering within a unified quantum simulation environment to achieve improved computational efficiency and scalability. By leveraging the parallelism of quantum circuits and the adaptability of classical optimization, Q-ClusterSim significantly reduces execution time while maintaining clustering accuracy. Simulations are conducted using IBM Qiskit and TensorFlow Quantum on benchmark datasets, where the proposed model consistently outperforms classical clustering algorithms in terms of convergence speed, precision, and resource consumption. Results validate the model’s effectiveness in managing complex data structures under limited qubit resources, making it suitable for real-world large data applications. This study highlights the transformative potential of quantum-assisted clustering in reshaping future data analytics and computational intelligence paradigms..
Quantum computers acting as ML accelerators have attracted considerable interest as a promising avenue for addressing the limitations of classical computing confronted with solving complex, high-dimensional problems and handling large data sets. The most exciting aspect of quantum computing lies in its quantum advantage via techniques such as quantum parallelism, superposition, and entanglement which allows not only for rapid data processing, but also a means to resolve complex optimization problems beyond the capacity of classical algorithms. Nevertheless, the usage of quantum computing in machine learning is still a fledgling domain, with challenges concerning quantum noise, hardware restrictions, and algorithmic development. In particular, this research is concerned with the development of and study on hybrid quantum-classical algorithms that target to improve ML models in terms of computational capabilities by making use of the best of both worlds. To address this, researchers are developing hybrid algorithms that leverage the strengths of quantum computing for specific tasks, like optimization and pattern recognition, while still relying on classical computing for more flexible and larger-scale processing, ultimately achieving more efficient machine learning systems that can handle large datasets and complex problem-solving more effectively. It includes potential hybrid approaches like quantum-enhanced optimization algorithms, quantum neural networks, and quantum support vector machines, and examines how such algorithms can be used for practical ML problems including data classification, regression and clustering. Furthermore, the paper proposes that hybrid quantum algorithms offer several advantages over their classical counterparts, such as faster convergence rates, higher accuracy in high-dimensional spaces, and improved handling of non-linear and complex problem landscapes. Key advancements in the area of data processing speed and efficiency in problem-solving with and without quantum in the machine learning workflow are also highlighted in the research through comparative analysis and simulation studies. Lastly, the paper concludes by outlining the obstacles yet to be surmounted and the opportunities that lie ahead for hybrid quantum-classical algorithms, such as further improvement of quantum hardware and error mitigation methods, as well as the design of new algorithmic paradigms that seamlessly integrates the classical and quantum computing spaces.
This paper investigates the application of quantum algorithms to enhance clustering performance on big data. Traditional clustering algorithms often struggle with the computational complexity associated with large datasets and intricate data distributions. We propose and analyze the implementation of quantum k-means and quantum hierarchical clustering algorithms, leveraging quantum superposition and entanglement to potentially achieve significant speedups. The theoretical framework outlines the core concepts and mathematical formulations of these algorithms. We explore the potential for quantum algorithms to address the limitations of classical approaches, particularly in scenarios involving high-dimensional data and complex clusters. The research focuses on the algorithmic design, examining the key steps involved in transforming classical clustering problems into quantum computations. This work contributes to the emerging field of quantum data mining and provides a foundational understanding of how quantum computing can revolutionize data analysis tasks. The primary focus is on the theoretical aspects of quantum clustering and does not include experimental validation.
This research focuses on the implementation of quantum machine learning with the classical models such as Gradient Boosting and K-means clustering for efficient classification and clustering of most complex datasets in advanced systems. Taking advantage of the large datasets that are handled by the qc, this work examines Quantum Support Vector Machines (QSVM), Quantum Boosting, and Quantum K-means. To compare the efficiency of these hybrid models three datasets - the healthcare, the financial, and the cyber-security datasets - are used. Our findings indicate that quantum optimization algorithms achieve better accuracy in clustering in comparison to the classical counterparts and are computationally faster. This work shows how quantum machine learning can lead to the enhancement of difficult data processing tasks, a major issue in the quantum computing domain, with specific reference to resources and high-dimensional data. The opportunity to integrate quantum and classical models successfully is the best basis for further developments in machine learning.