Unsupervised machine learning is one of the main techniques employed in artificial intelligence. We introduce an algorithm for quantum-assisted unsupervised data clustering using the self-organizing feature map, a type of artificial neural network. The complexity of our algorithm scales as $O(LN)$, in comparison to the classical case which scales as $O(LMN)$, where $N$ is the number of samples, $M$ is the number of randomly sampled cluster vectors, and $L$ is the number of the shifts of cluster vectors. We perform a proof-of-concept demonstration of one of the central components on the IBM quantum computer and show that it allows us to reduce the number of calculations in the number of clusters. Our algorithm exhibits exponential decrease in the errors of the distance matrix with the number of runs of the algorithm.
Unsupervised machine learning is one of the main techniques employed in artificial intelligence. We introduce an algorithm for quantum-assisted unsupervised data clustering using the self-organizing feature map, a type of artificial neural network. The complexity of our algorithm scales as O(LN), in comparison to the classical case which scales as O(LMN), where N is the number of samples, M is the number of randomly sampled cluster vectors, and L is the number of the shifts of cluster vectors. We perform a proof-of-concept demonstration of one of the central components on the IBM quantum computer and show that it allows us to reduce the number of calculations in the number of clusters. Our algorithm exhibits exponential decrease in the errors of the distance matrix with the number of runs of the algorithm.
Recent progress in machine learning has affected almost all areas of the modern economy. The use of quantum protocols to speed up classical machine learning approaches may have further profound effects on society in the future. Here, we developed a hybrid quantum-assisted self-organizing feature map, a type of artificial neural network, and apply it to the data clustering problem in an unsupervised manner. We show that it allows us to reduce the number of calculations in a number of clusters. It is believed that similar types of hybrid quantum classical algorithms can be the main test bed to achieve practical quantum supremacy on Noisy Intermediate Scale Quantum devices.
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over the corresponding classical algorithms. In this paper, we introduce q-means, a new quantum algorithm for clustering which is a canonical problem in unsupervised machine learning. The q-means algorithm has convergence and precision guarantees similar to k-means, and it outputs with high probability a good approximation of the k cluster centroids like the classical algorithm. Given a dataset of Nd-dimensional vectors vi (seen as a matrix V∈RN×d) stored in QRAM, the running time of q-means is O(kdδ2ηκ(V)(μ(V)+kδη)+k2δ2η1.5κ(V)μ(V)) per iteration, where κ(V) is the condition number, μ(V) is a parameter that appears in quantum linear algebra procedures and η=maxi∣∣vi∣∣2. For a natural notion of well-clusterable datasets, the running time becomes O(k2dδ3η2.5+k2.5δ3η2) per iteration, which is linear in the number of features d, and polynomial in the rank k, the maximum square norm η and the error parameter δ. Both running times are only polylogarithmic in the number of datapoints N. Our algorithm provides substantial savings compared to the classical k-means algorithm that runs in time O(kdN) per iteration, particularly for the case of large datasets.
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over the corresponding classical algorithms. In this paper, we introduce q-means, a new quantum algorithm for clustering which is a canonical problem in unsupervised machine learning. The q-means algorithm has convergence and precision guarantees similar to k-means, and it outputs with high probability a good approximation of the k cluster centroids like the classical algorithm. Given a dataset of Nd-dimensional vectors vi (seen as a matrix V∈RN×d) stored in QRAM, the running time of q-means is O(kdδ2ηκ(V)(μ(V)+kδη)+k2δ2η1.5κ(V)μ(V)) per iteration, where κ(V) is the condition number, μ(V) is a parameter that appears in quantum linear algebra procedures and η=maxi∣∣vi∣∣2. For a natural notion of well-clusterable datasets, the running time becomes O(k2dδ3η2.5+k2.5δ3η2) per iteration, which is linear in the number of features d, and polynomial in the rank k, the maximum square norm η and the error parameter δ. Both running times are only polylogarithmic in the number of datapoints N. Our algorithm provides substantial savings compared to the classical k-means algorithm that runs in time O(kdN) per iteration, particularly for the case of large datasets.
Clustering is one of the most fundamental tasks in machine learning, and the k-means clustering algorithm is perhaps one of the most widely used clustering algorithms. However, it suffers from several limitations, such as sensitivity to centroid initialization, difficulty capturing non-linear structure, and poor performance in high-dimensional spaces. Recent work has proposed improved initialization strategies and quantum-assisted distance computation, but the similarity metric itself has largely remained classical. In this study, we propose a quantum-enhanced variant of k-means that replaces the Euclidean distance with a quantum kernel derived from the inner product between feature-mapped quantum states. Using the Iris dataset, we use multiple quantum feature maps, including entangled SU2 and ZZ circuits, to embed classical data into a higher-dimensional Hilbert space where cluster structures become more separable. We will also be testing using another dataset, namely the breast cancer dataset. Similarity between data points is computed through the inner product between two states. Our results show that this approach achieves improved clustering stability and competitive accuracy compared to the classical algorithm, with the SU2 feature map yielding an accuracy of 88.6 % on the Iris dataset and 91.0 % on the breast cancer dataset, despite operating on NISQ-feasible shallow circuits. These findings suggest that quantum kernels provide a richer similarity landscape than traditional distance metrics, offering a promising path toward more robust unsupervised learning in the NISQ era.
A quantum self-organization feature mapping networks model and its clustering algorithm are presented.Both the input and the weight of the model are represented by the quantum bits,and the output of the model is represented by the real number.The model is composed of input layer and competitive layer.Firstly,the samples are transformed into quantum states and transported to the input layer,and then the similar coefficients of quantum states are computed between the input and the weight.Secondly,the competitive layer extracts the implicit pattern characters of the clustering samples and takes self-organization to them, and then output the clustering result.The quantum states of weight are modified by quantum rotation gates.The networks are trained by the algorithm of the unsupervised learning and supervised learning together.Finally two simulation experiments demonstrate that the model and algorithm are evidently superior to the general self-organization feature mapping networks.
Quantum computing exploits superposition, entanglement, and interference to address problems beyond classical reach, yet current devices are limited by noise and scale. Hybrid quantum–classical approaches therefore play a key role in achieving near-term utility by integrating quantum subroutines into classical workflows. Within this setting, Quantum Artificial Intelligence (QAI) offers new opportunities for machine learning. This thesis focuses on unsupervised Quantum Machine Learning, motivated by the abundance of unlabeled data and the importance of tasks such as clustering, dimensionality reduction, and anomaly detection. We study how to design hardware-efficient quantum subroutines, identify unsupervised paradigms well suited to hybrid computation, and assess potential advantages over classical methods. The contributions include a critical review of existing QAI approaches, the development of shallow-depth quantum subroutines for core operations, and the proposal of hybrid algorithms evaluated on synthetic and real datasets. The results highlight when quantum components provide practical value and clarify trade-offs between performance and complexity under current hardware constraints.