Quantum Fuzzy K-Means Algorithm Based on Fuzzy Theory

Cluster analysis is used to classification according to their different charac-teristics, affinity, and similarity. Because the boundary of the relationship between things is often unclear, it is inevitable to use the fuzzy method to perform cluster analysis. In this paper, according to the cross fusion of "fuzzy theory + K-means algorithm + quantum computing", a quantum fuzzy k-means algorithm based on fuzzy theory is proposed for the first time, which can classify samples with lower time complexity and higher ac-curacy. Firstly, the training data sets and the classified sample points can be encoded into quantum states, and swap test is used to calculate the similarity between the classified sample points and k cluster centers with high parallel computing abilities. Secondly, the similarity is stored with the form of quan-tum bits by using the phase estimation algorithm. The Grover algorithm is used to search the cluster points with the highest membership degree and de-termine the category of the test samples. Finally, by introducing quantum computing theory, the computation complexity of the proposed algorithm is improved, and the space complexity of the proposed algorithm is reduced. By introducing fuzzy theory, the proposed algorithm can deal with uncertain problems efficiently, the scope of application of the algorithm is expanded, and the accuracy is improved.