基于量子模距离的量子态聚类识别

针对量子系统的状态识别，定义了一种量子模距离作为量子态之间的相似性度量，提出了一种基于量子模距离的聚类算法，它既适用于对量子叠加态的识别，也适合对量子纠缠态的识别。在算法中，根据待识别的样本量子态求取聚类中心，分别计算各量子态到聚类中心的量子模距离，根据量子模距离对量子态进行聚类识别。算例说明了这种聚类识别方法的合理性和有效性。

Clustering Recognition of Quantum States Based on Quantum Module Distance

In view of recognition of states of quantum systems, a kind of quantum module distance, which is used as a measurement of comparability between two quantum states, is defined and a kind of clustering algorithm based on quantum module distance is proposed. This algorithm is suitable for recognition of both quantum superposition states and quantum entangled states.In this algorithm, firstly calculate the clustering center according to the samples of quantum states which need recognizing. Secondly calculate quantum module distance between every quantum state and the clustering center. Lastly recognize quantum states according to quantum module distances. An example is given to demonstrate the reasonableness and effectiveness of the clustering method for recognition of quantum states.