Granular-balls reduce the data volume and enhance the efficiency of fundamental algorithms such as clustering and classification. However, generating granular-balls is a time-consuming process, posing a significant bottleneck for the practical application of granular-balls. In this paper, we propose two innovative quantum granular-ball generation methods that capitalize on the inherent properties of quantum computing. The first method employs an iterative splitting technique, while the second utilizes a predetermined number of splits. The iterative splitting method significantly reduces time complexity compared to existing classical granular-ball generation methods. Notably, the method employing a fixed number of splits delivers a substantial quadratic acceleration over the iterative technique. Moreover, we also propose a quantum k-nearest neighbors algorithm based on granular-balls (QGBkNN) and empirically show the effectiveness of our approach.
Granular-balls reduce the data volume and enhance the efficiency of fundamental algorithms such as clustering and classification. However, generating granular-balls is a time-consuming process, posing a significant bottleneck for the practical application of granular-balls. In this paper, we propose two innovative quantum granular-ball generation methods that capitalize on the inherent properties of quantum computing. The first method employs an iterative splitting technique, while the second utilizes a predetermined number of splits. The iterative splitting method significantly reduces time complexity compared to existing classical granular-ball generation methods. Notably, the method employing a fixed number of splits delivers a substantial quadratic acceleration over the iterative technique. Moreover, we also propose a quantum k-nearest neighbors algorithm based on granular-balls (QGBkNN) and empirically show the effectiveness of our approach.
High time complexity is one of the biggest challenges faced by k-Nearest Neighbors (kNN). Although current classical and quantum kNN algorithms have made some improvements, they still have a speed bottleneck when facing large amounts of data. To address this issue, we propose an innovative algorithm called Granular-Ball based Quantum kNN(GB-QkNN). This approach achieves higher efficiency by first employing granular-balls, which reduces the data size needed to processed. The search process is then accelerated by adopting a Hierarchical Navigable Small World (HNSW) method. Moreover, we optimize the time-consuming steps, such as distance calculation, of the HNSW via quantization, further reducing the time complexity of the construct and search process. By combining the use of granular-balls and quantization of the HNSW method, our approach manages to take advantage of these treatments and significantly reduces the time complexity of the kNN-like algorithms, as revealed by a comprehensive complexity analysis.
QGB-WkNN: Quantum Granular-Ball Learning for Robust Classification
Nearest-neighbor classification is widely used in machine learning, yet existing methods often suffer from low computational efficiency and limited robustness in noisy environments. To jointly address these challenges, this paper proposes an efficient and reliable weighted K-nearest neighbor classification framework based on quantum granular balls, termed QGB-WkNN. The proposed framework improves computational efficiency by integrating quantum-enhanced granular-ball representation with hierarchical nearest-neighbor search, while enhancing classification reliability through a purity-aware weighted decision mechanism. Specifically, quantum-kernel granular balls are constructed to reduce retrieval redundancy and strengthen nonlinear feature representation under limited quantum resources. A granular-ball purity-guided HNSW optimization strategy is developed to exploit structural reliability for hierarchical graph construction during neighbor retrieval, alleviating the local optimality issue caused by conventional random layering. Finally, a weighted voting mechanism jointly incorporating granular-ball similarity and purity is introduced to produce more reliable classification decisions in noisy environments. Extensive experiments on benchmark datasets demonstrate that QGB-WkNN achieves competitive classification accuracy while exhibiting favorable Pareto trade-offs between classification performance and computational cost. Moreover, the proposed framework consistently improves robustness under various noisy conditions, suggesting that reliability-aware quantum granular-ball learning provides a promising paradigm for efficient and robust nearest-neighbor classification.
Quantum clustering aims to exploit quantum feature representations to uncover complex data structures beyond conventional Euclidean geometry. Yet this sample-level kernel construction requires O(n^2) quantum circuit executions for n data points, creating a major bottleneck under near-term quantum resource constraints. Prior solutions fail to resolve this efficiency-accuracy dilemma: classical granular-ball clustering reduces sample complexity but relies on Euclidean metrics that cannot capture quantum correlations, while existing quantum compression schemes prioritize efficiency over structural preservation, degrading performance on non-convex or noisy data. Here we propose Granular-Ball Quantum Clustering (GBQC), a framework that tightly couples granular-ball structural abstraction with quantum feature learning. GBQC first compresses raw data into compact, representative granular balls via a PCA-guided splitting strategy, reducing kernel evaluations by 80% compared to full-sample methods. A quantum cohesion mechanism then filters noisy granules in Hilbert space to improve clustering robustness. Extensive experiments on synthetic, noisy, overlapping, and real-world datasets demonstrate that GBQC consistently achieves superior clustering accuracy and robustness compared with representative classical and quantum clustering methods. Meanwhile, the proposed granular-ball compression significantly reduces quantum kernel evaluations and computational overhead, enabling quantum clustering experiments on larger datasets within parameterized quantum learning frameworks. These results suggest that granular-ball representations serve not only as a compression mechanism to reduce quantum computational costs but also as an effective structural abstraction mechanism that improves clustering quality by eliminating redundant and structurally ambiguous learning units.
The KNN (K-nearest neighbors) algorithm is one of Top-10 data mining algorithms and is widely used in various fields of artificial intelligence. This leads to that quantum KNN algorithms have developed and achieved certain speed improvements, denoted as Q-KNN. However, these Q-KNN methods must face two key problems as follows. The first one is that they are mainly focused on neighbor selection without paying attention to the influence of K value on the algorithm. The second is that only the neighbor selection process is quantized, and the selection of K value is not quantized. To solve these problems, this paper designs a novel quantum circuit for KNN classification, so as to simultaneously quantumize the neighbor selection and K value selection process. Specifically, the least squares loss and sparse regularization term are first used to construct the objective function of the proposed quantum KNN, so that it can simultaneously obtain the optimal K value and K nearest neighbors of the testing data. And then, a new quantum circuit is proposed to quantumize the process through quantum phase estimation, controlled rotation, and inverse phase estimation techniques. Finally, experiments are conducted with qiskit and matlab to output the quantum and classical results of the algorithm, verifying that the proposed algorithm can output the optimal K value and K nearest neighbors for each testing data.
Mahalanobis distance is a distance measure that takes into account the relationship between features. In this paper, we proposed a quantum KNN classification algorithm based on the Mahalanobis distance, which combines the classical KNN algorithm with quantum computing to solve supervised classification problem in machine learning. Firstly, a quantum sub-algorithm for searching the minimum of disordered data set is utilized to find out K nearest neighbors of the testing sample. Finally, its category can be obtained by counting the categories of K nearest neighbors. Moreover, it is shown that the proposed quantum algorithm has the effect of squared acceleration compared with the classical counterpart.
Quantum computing has risen as the new type of computer that theoretically reduces the time complexity of classical methods exponentially because of the nature of superposition. It is promising to reduce runtimes on large data sets in machine learning (ML). Meanwhile, k-nearest neighbor (kNN) is a simple ML algorithm that can be translated to a quantum version (QkNN) to perform classification tasks efficiently. Here, we show a new version of QkNN which has a speed up in time complexity by using a new design of quantum circuits called integrated swap test. This quantum circuit can load two N-dimensional states and calculate the fidelity between them. Results show that QkNN allows us to take a different approach to the ML field.