Quantum k-Means Clustering Using Hadamard-Test-Based Similarity Estimation

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.