Quantum divisive hierarchical clustering based on Manhattan distance

Zhihao Wu, Tingting Song, Yanbing Zhang

Fengbo Kong, Hong Lai, Hailing Xiong

It is getting harder to deal with the large data sets by the classical hierarchical clustering algorithm, so we propose an efficient quantum hierarchical clustering algorithm, in which the quantum bit (qubit) is used to represent the data point in the space.For quantum entanglement, the distance between two data points is calculated through adding an auxiliary particle to construct the entangled state.Then a projective measurement is performed on the auxiliary particle alone.The distance between two points is acquired by the projective measurement.We use the distance of the cluster centroids as a measure of similarity between clusters.Also, based on the principle of the minimum cluster centroids distance, the nearest two clusters are merged.We aim at improving time and space complexity and effect of the clustering of the hierarchical clustering algorithm.

Wen Liu, Wei Zhang

Secure Manhattan distance computation allows two parties to privately compute the Manhattan distance of their points, which is important and has broad applications. In this paper, we present a protocol for secure Manhattan distance computation based on phase shift operation. Because of quantum mechanics' physical principle, our protocol can also resist outside attacks and don't leak any private information of participants.

Péter Wittek

Kaoutar Benlamine, Younès Bennani, Ahmed Zaiou +3 more

Mochamad Wahyudi, Imeldi Sintagel br Sianipar, Lise Pujiastuti +2 more

Acquired Immunodeficiency Syndrome (AIDS) caused by the Human Immunodeficiency Virus (HIV) is one of the deadliest infectious diseases in the world. Understanding its spread and epidemiological characteristics is crucial for developing and preventing more effective treatments. This study uses the K-Medoids method with a quantum computing approach to predict AIDS based on clinical and demographic data. K-Medoids is chosen to group large amounts of data using a clustering technique that determines the center point (medoid) of each cluster, minimizing the overall distance between data in a cluster. The Manhattan distance is used because it is easier to process data. The quantum computing approach is used to overcome the limitations of classical computing when processing large-scale medical data. This study shows that the application of quantum algorithms to the K-Medoids method allows for faster and more accurate predictions in the diagnosis of AIDS. The tests carried out showed that the prediction accuracy of classical and quantum methods was comparable, namely 85%. The results support the great potential of quantum computing to improve the efficiency of medical predictions. The research involves converting data into quantum format, processing it with the K-Medoids algorithm, and evaluating its performance based on metrics such as intercluster distance and computation time. The research will also identify patterns and risk factor for the spread of AIDS that can be used to develop more effective health interventions. The conclusion of the research is that integrating the K-Medoids techniques can only increase the speed of data processing but also provide competitive accuracy compared to traditional techniques. This research opens up new possibilities in medical data analysis, especially when managing large and complex data sets. The bottom line is that these findings can help make better medical decisions and strategically support AIDS prevention and treatment efforts.