Innovative Quantum K-Means Clustering Using a Multi-Distance Measurement Circuit

This paper, presents a novel multi-distance measuring quantum circuit applied to the K-means algorithm. Our proposed quantum K-means algorithm eliminates the need for oracles or quantum RAM, setting it apart from traditional quantum methods. By utilizing inverse stereographic projection, our approach prepares data for quantum circuits while preserving relative distances between data points. Additionally, we introduce a generalized algorithm to build a quantum circuit that facilitates the parallel measurement of distances from one point to multiple others. We evaluate the effectiveness of our circuit as a part of K-means algorithm on both separable and inseparable datasets, assessing its performance across different scenarios.