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Asia-Pacific Conference on Image Processing, Electronics and Computers (IPEC)

Quantum K-Means Model based on Optimization Framework

Zexiang Shao, Shibin Zhang, Sachin Kumar

Published Apr 14, 2023• 3 citations
Publisher

Abstract

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.

DOI
10.1109/ipec57296.2023.00071

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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.
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.
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 paper introduces an adaptive quantum algorithm probability model, designed to enhance the optimization and stability of quantum algorithms. Traditional quantum algorithms often rely on static parameters, while this research focuses on probabilistic models, enabling efficient parameter tuning and improved performance. We present a framework for constructing probabilistic models that translate quantum algorithm execution into distribution functions, leveraging the inherent properties of probability to guide optimization. The core mechanism centers around exploiting quantum algorithms' unique characteristics to create a probabilistic representation of the computation, enabling targeted parameter adjustments to improve algorithm performance. The novel contribution lies in the integration of this probabilistic model into a robust optimization framework, addressing a critical challenge in the design and application of quantum algorithms.
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.
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Quantum computing is a promising and emerging field of computer science with the potential to improve artificial intelligence techniques, particularly those related to optimization. However, current quantum devices operate in the Noisy Intermediate-Scale Quantum era, in which quantum noise can significantly compromise computational reliability. Evolutionary algorithms are inherently stochastic and may therefore be less sensitive to such noise, or even benefit from it. This study evaluates the performance of a hybrid quantum genetic algorithm on a set of combinatorial and continuous optimization problems under various realistic noise models. The findings demonstrate that quantum noise does not hinder the algorithm's performance and can even enhance its exploratory capabilities in some cases. This suggests that noise-aware quantum evolutionary strategies have the potential to be effective even with today's imperfect quantum hardware.