Abstract: Quantitative reconstruction of classical machine learning algorithms is one of the significant research directions in the field of quantum machine learning.The quantitative implementation of clustering algorithm,which has been widely used in the machine learning area,is worth studying.Most of the current quantum machine learning algorithms suffer from the difficulty of reproduction and the difficulty of forming direct comparisons with classical algorithms.To address these problems,this paper proposes the quantum prototype clustering algorithm that can be easily deployed on existing general-purpose quantum computing devices.Combining the rotation property of single quantum bit(qubit),and finding the feature mapping method with minimal information loss,the single qubit rotation is created using two-dimensional feature data.Then,based on the properties of multi-qubit entanglement and the collapse of the entangled system,a quantum circuit is designed for generating a specific quantum entangled system and measuring the collapsed result of entangled system.Based on the relationship between the rotation angle of controlled qubits in the entangled system and the collapse result of the entangled system,and combined with the definition of Minkowski distance,a quantum distance for evaluating the similarity of input samples is then derived.Both the quantum distance calculation module and its counterpart in classic computer have the same forms of input and output,so that the latter can be replaced by the former without modification,hence the prototype clustering algorithm is quantitatively reconstructed into QPC.Several replicated experiments on multiple publicly available datasets from kaggle and scikit-learn show that the QPC performs similarly to classic prototype clustering algorithm in terms of many evaluation metrics,such as the mean sample-centroid distance.

Key words: Quantum computation, Quantum machine learning, Clustering algorithm, Prototype clustering