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Acta Sinica Quantum Optica

Clustering Recognition of Quantum States Based on Quantum Module Distance

Zonghai Chen

Published Jan 1, 2003• 3 citations
OpenAlex

Abstract

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.

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•Aug 31, 2026•0 citations
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.
Looking upon every encoding state of quantum information systems as a quantum information pattern, A kind of pattern-distance between different patterns as a measurement of comparability of quantum information patterns is defined, and two kinds of recognition algorithms based on pattern-distance for quantum information are proposed. They can respectively recognize quantum information with known objective pattern and unknown objective pattern. In the two algorithms, the phases and occurrence probabilities of different eigenpatterns of quantum information are sufficiently considered. Two examples demonstrate the feasibility and effectiveness of the two recognition methods. These algorithms point out a new and important path for applications of quantum information and pattern recognition.
The paper proposes a quantum enhanced solution method based on quantum K-means for platform clustering and grouping in joint operations campaigns. The method first calculates the number of categories for platform clustering based on the determined number of task clusters, and sets the number of clustering categories in the classical K-means algorithm. By using the location information of the tasks, the clustering center points are calculated and derived. Secondly, the Euclidean distance is used as an indicator to measure the distance between the platform data and each cluster center point. The platform data are quantized and transformed into their corresponding quantum state representations. According to theoretical derivation, the Euclidean distance solution is transformed into the quantum state inner product solution. By designing and constructing a universal quantum state inner product solution quantum circuit, the Euclidean distance solution is completed. Then, based on the sum of squared errors of the clustering dataset, the corresponding quantum circuits are constructed through calculation and deduction. The experimental results show that compared with the classical K-means algorithm, the proposed method not only effectively solves the platform clustering and grouping problem on such action scales, but also significantly reduces the time and space complexity of the algorithm.
It is getting harder to deal with the large data sets by the classical hierarchical clustering algorithm, so we propose an efficient quantum hierarchical clustering algorithm, in which the quantum bit (qubit) is used to represent the data point in the space.For quantum entanglement, the distance between two data points is calculated through adding an auxiliary particle to construct the entangled state.Then a projective measurement is performed on the auxiliary particle alone.The distance between two points is acquired by the projective measurement.We use the distance of the cluster centroids as a measure of similarity between clusters.Also, based on the principle of the minimum cluster centroids distance, the nearest two clusters are merged.We aim at improving time and space complexity and effect of the clustering of the hierarchical clustering algorithm.
Abstract Quantum state clustering provides a powerful tool for quantum information processing. This paper focuses on the classification of single-qubit pure and mixed states via clustering algorithms, and discovers that the classical K -means algorithm has two limitations in clustering quantum states: the Euclidean distance cannot accurately reflect the similarity between quantum states, and the centroid update based on the arithmetic mean frequently fails to yield valid quantum states. To address these issues, we propose two distance metrics for quantum states: the dynamic distance and the Bloch distance, and adopt the K -medoids method to update the centroid, ensuring that the cluster center always remains a valid quantum state, thereby designing a quantum-data-adaptive clustering algorithm. Experimental results show that the dynamic distance achieves a clustering accuracy as high as 91.4 % , but at the cost of higher computational complexity. In contrast, the Bloch distance significantly reduces computational complexity while maintaining clustering performance comparable to that of the dynamic distance, achieving a clustering accuracy of 87.4 % . This paper provides a practical method for achieving efficient and reliable clustering of single-qubit quantum states.
The paper proposes a quantum enhanced solution method based on quantum K-means for platform clustering and grouping in joint operations campaigns. The method first calculates the number of categories for platform clustering based on the determined number of task clusters, and sets the number of clustering categories in the classical K-means algorithm. By using the location information of the tasks, the clustering center points are calculated and derived. Secondly, the Euclidean distance is used as an indicator to measure the distance between the platform data and each cluster center point. The platform data is quantized and transformed into the corresponding quantum state representation. According to theoretical derivation, the Euclidean distance solution is transformed into the quantum state inner product solution. By designing and constructing a universal quantum state inner product solution quantum circuit, the Euclidean distance solution is completed. Then, based on the sum of squared errors of the clustering dataset, the corresponding quantum circuits are constructed through calculation and deduction. The experimental results show that the proposed method not only effectively solves the platform clustering and grouping problem under such action scales, but also significantly reduces the time and space complexity of the algorithm compared to the classical K-means algorithm.
Traditional clustering algorithms, such as k-means and DBSCAN, often face significant challenges when applied to big data. The computational complexity associated with distance calculations and nearest neighbor searches scales poorly with dataset size, limiting their effectiveness. This paper proposes a novel approach to clustering inspired by quantum measurement theory, specifically quantum-inspired nearest neighbor search. We leverage concepts from quantum mechanics, such as superposition and measurement, to design clustering algorithms that can efficiently identify clusters within high-dimensional datasets. The core idea is to treat the clustering problem as a measurement process, where candidate cluster centers are repeatedly measured against data points, and the most likely cluster centers are selected. The resulting algorithms aim to provide scalability improvements over conventional methods, particularly for datasets with a large number of features and data points. The effectiveness of the proposed algorithms is demonstrated through theoretical analysis and conceptual explanations, highlighting the potential benefits and future research directions.