A hybrid classical-quantum clustering algorithm based on quantum walks

The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum walk (QW) with the problem of data clustering, and develop two clustering algorithms based on the one-dimensional discrete-time QW. Then, the position probability distributions induced by QW in these algorithms are investigated, which also indicates the possibility of obtaining better results. Consequently, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.