Improvement of K-means Clustering Algorithm Based on Quantum State Similarity Measurement

The classical K-means clustering algorithm is widely used in various fields due to its simple implementation and efficient computation, but the classical K-means clustering algorithm relies on the random selection of the initial center of mass, which is prone to fall into the deadlock of local optimality. In order to break through this limitation, the quantum K-means clustering algorithm is introduced, which is able to explore multiple potential clustering center combinations at the same time through the parallelism of quantum computation, so as to have a greater probability of converging to the globally optimal solution. Quantum K-means clustering algorithms typically employ fidelity as a similarity measure between quantum states, and similarity is assessed by calculating the probability of overlap between quantum states. However, the fidelity only quantizes the pure state information of the quantum states and ignores the classical statistical features of the data itself, which may lead to unreasonable clustering boundaries in mixed state or noise interference scenarios. In response to the above problems, this paper proposes an improved quantum-classical hybrid similarity metric, whose core idea is to incorporate the dual constraints of quantum information and classical features.