The quantization reconstruction of classical machine learning algorithms is an important research direction in quantum machine learning. Clustering, a widely applied algorithm in machine learning, also holds high research value when quantized. Currently, most quantum machine learning algorithms, including those employing
AI techniques, face challenges such as difficulty in replication and the lack of intuitive comparisons with classical algorithms. A quantum prototype clustering algorithm (QPC) is proposed to address these issues, which can be easily deployed on existing general-purpose quantum computing devices. This approach first utilizes single-qubit rotation properties to find the feature mapping with minimal information loss, creating single-qubit rotations from two-dimensional feature data. Then, based on the characteristics of multi-qubit entanglement and entanglement system collapse, a quantum circuit for generating specific quantum entanglement systems and measuring the collapse results of entanglement systems is designed. By establishing the relationship between controlled qubit rotation angles in the entanglement system and the collapse results of the entanglement system and combining the definition of Minkowski distance, a quantum distance is derived for evaluating the similarity of input samples. The quantum distance measurement module, with the same input-output format as the distance calculation module in classical computers, can directly replace the Minkowski distance calculation in prototype clustering without modification, thus reconstructing classical prototype clustering algorithms, with AI included, into QPC. Multiple repeated experiments on publicly available datasets from Kaggle and Scikitlearn demonstrate that with AI integration, QPC exhibits no significant differences in evaluation metrics, such as average sample centre distance, compared to classical prototype clustering algorithms.
Quantum probability provides a novel framework for formulating machine-learning (ML) problems in Hilbert space. We introduce a prototype-based learning scheme where class representatives are encoded as generative matrix product states (MPS). Because these prototypes reside in the same Hilbert space as quantum-encoded data samples, various ML tasks such as classification and clustering can be performed through geometric measures of quantum states. This approach lifts prototype learning from classical feature space to quantum Hilbert space. Benchmarks on Fashion-MNIST and a real-world electrocardiogram dataset demonstrate that our method outperforms classical prototype approaches while remaining competitive with standard black-box neural networks. We also identify an ``attraction'' effect induced by the quantum-probabilistic prototypes and introduce a dimensionality-reduction scheme based on prototype distances. Our results establish quantum states as an explainable framework for prototype learning, opening new directions for designing ML algorithms in quantum Hilbert space.