Quantum Cluster Algorithm for Data classification

We present a quantum algorithm for data classification based on the nearest-neighbor learning algorithm. The classification algorithm is divided into two steps: Firstly, data in the same class is divided into smaller groups with sublabels assisting building boundaries between data with different labels. Secondly we construct a quantum circuit for classification that contains multi control gates. The algorithm is easy to implement and efficient in predicting the labels of test data. To illustrate the power and efficiency of this approach, we construct the phase transition diagram for the metal-insulator transition of $VO_2$, using limited trained experimental data, where $VO_2$ is a typical strongly correlated electron materials, and the metallic-insulating phase transition has drawn much attention in condensed matter physics. Moreover, we demonstrate our algorithm on the classification of randomly generated data and the classification of entanglement for various Werner states, where the training sets can not be divided by a single curve, instead, more than one curves are required to separate them apart perfectly. Our preliminary result shows considerable potential for various classification problems, particularly for constructing different phases in materials.