Abstract Faster than classical algorithms, quantum algorithms benefit from the superposition property of quantum information to offer significant speedup to complex algorithms. Therefore, quantum computing can be used to help machine learning algorithms by boosting their performance and accelerate the processing of time‐consuming ones. Clustering algorithms are very complex unsupervised learning algorithms. Indeed, the similarity calculation (distance) between input vectors is a resource‐consuming step, especially when working with large datasets. In this article, we propose a new better‐performing recommender system that operates as a combination of an adapted quantum K‐means algorithm and the singular value decomposition (SVT) algorithm. We integrate the developed quantum clustering algorithm to a prediction process of the proposed recommender system using matrix completion. To the best of our knowledge, no system with such details was proposed in the literature. The system was applied on the MovieLens dataset without a dimensionality reduction step and evaluated according to measures of information retrieval systems. The results of the quantum K‐means algorithm show that the quantum version leads to a logarithmic reduction of the time complexity compared to the classical algorithm. The proposed system has proved to be better than the previous tested ones in terms of precision and recall.
Abstract Faster than classical algorithms, quantum algorithms benefit from the superposition property of quantum information to offer significant speedup to complex algorithms. Therefore, quantum computing can be used to help machine learning algorithms by boosting their performance and accelerate the processing of time‐consuming ones. Clustering algorithms are very complex unsupervised learning algorithms. Indeed, the similarity calculation (distance) between input vectors is a resource‐consuming step, especially when working with large datasets. In this article, we propose a new better‐performing recommender system that operates as a combination of an adapted quantum K‐means algorithm and the singular value decomposition (SVT) algorithm. We integrate the developed quantum clustering algorithm to a prediction process of the proposed recommender system using matrix completion. To the best of our knowledge, no system with such details was proposed in the literature. The system was applied on the MovieLens dataset without a dimensionality reduction step and evaluated according to measures of information retrieval systems. The results of the quantum K‐means algorithm show that the quantum version leads to a logarithmic reduction of the time complexity compared to the classical algorithm. The proposed system has proved to be better than the previous tested ones in terms of precision and recall.
Abstract Tensors are increasingly ubiquitous in various areas of applied mathematics and computing, and tensor decompositions are of practical significance and benefit many applications in data completion, image processing, computer vision, collaborative filtering, etc. Recently, Kilmer and Martin propose a new tensor factorization strategy, tensor singular value decomposition (t-svd), which extends the matrix singular value decomposition to tensors. However, computing t-svd for high dimensional tensors costs much computation and thus cannot efficiently handle large scale datasets. Motivated by advantage of quantum computation, in this paper, we present a quantum algorithm of t-svd for third-order tensors and then extend it to order-p tensors. We prove that our quantum t-svd algorithm for a third-order N dimensional tensor runs in time N polylog ( N ) if we do not recover classical information from the quantum output state. Moreover, we apply our quantum t-svd algorithm to context-aware multidimensional recommendation systems, where we just need to extract partial classical information from the quantum output state, thus achieving low time complexity.
This research focuses on the implementation of quantum machine learning with the classical models such as Gradient Boosting and K-means clustering for efficient classification and clustering of most complex datasets in advanced systems. Taking advantage of the large datasets that are handled by the qc, this work examines Quantum Support Vector Machines (QSVM), Quantum Boosting, and Quantum K-means. To compare the efficiency of these hybrid models three datasets - the healthcare, the financial, and the cyber-security datasets - are used. Our findings indicate that quantum optimization algorithms achieve better accuracy in clustering in comparison to the classical counterparts and are computationally faster. This work shows how quantum machine learning can lead to the enhancement of difficult data processing tasks, a major issue in the quantum computing domain, with specific reference to resources and high-dimensional data. The opportunity to integrate quantum and classical models successfully is the best basis for further developments in machine learning.
In this paper, we present a quantum singular value decomposition algorithm for third-order tensors inspired by the classical algorithm of tensor singular value decomposition (t-svd) and then extend it to order-p tensors. It can be proved that the quantum version of the t-svd for a third-order tensor A∈RN×N×N achieves the complexity of O(Npolylog(N)), an exponential speedup compared with its classical counterpart. As an application, we propose a quantum algorithm for recommendation systems which incorporates the contextual situation of users to the personalized recommendation. We provide recommendations varying with contexts by measuring the output quantum state corresponding to an approximation of this user's preferences. This algorithm runs in expected time O(Npolylog(N)poly(k)), if every frontal slice of the preference tensor has a good rank-k approximation. At last, we provide a quantum algorithm for tensor completion based on a different truncation method which is tested to have a good performance in dynamic video completion.
The exponential growth of data and the increasing complexity of high-dimensional classification problems have pushed classical computing methods to their limits. Quantum computing emerges as a promising paradigm to address these challenges. This research article explores advanced quantum algorithms for big data clustering and high-dimensional classification. We investigate quantum versions of K-means, spectral clustering, and support vector machines, comparing their performance with classical counterparts. Our results demonstrate significant speedups in processing time and improvements in clustering quality for high-dimensional datasets. Additionally, we propose a novel quantum-inspired classical algorithm that bridges the gap between quantum and classical approaches. This comprehensive study provides insights into the potential of quantum computing in revolutionizing data analysis and machine learning, paving the way for future advancements in the field.
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.