Physicists use quantum models to describe the behavior of physical systems. Quantum models owe their success to their interpretability, to their relation to probabilistic models (quantization of classical models) and to their high predictive power. Beyond physics, these properties are valuable in general data science. This motivates the use of quantum models to analyze general nonphysical datasets. Here we provide both empirical and theoretical insights into the application of quantum models in data science. In the theoretical part of this paper, we firstly show that quantum models can be exponentially more efficient than probabilistic models because there exist datasets that admit low-dimensional quantum models and only exponentially high-dimensional probabilistic models. Secondly, we explain in what sense quantum models realize a useful relaxation of compressed probabilistic models. Thirdly, we show that sparse datasets admit low-dimensional quantum models and finally, we introduce a method to compute hierarchical orderings of properties of users (e.g., personality traits) and items (e.g., genres of movies). In the empirical part of the paper, we evaluate quantum models in item recommendation and observe that the predictive power of quantum-inspired recommender systems can compete with state-of-the-art recommender systems like SVD++ and PureSVD. Furthermore, we make use of the interpretability of quantum models by computing hierarchical orderings of properties of users and items. This work establishes a connection between data science (item recommendation), information theory (communication complexity), mathematical programming (positive semidefinite factorizations) and physics (quantum models).
Physicists use quantum models to describe the behavior of physical systems. Quantum models owe their success to their interpretability, to their relation to probabilistic models (quantization of classical models) and to their high predictive power. Beyond physics, these properties are valuable in general data science. This motivates the use of quantum models to analyze general nonphysical datasets. Here we provide both empirical and theoretical insights into the application of quantum models in data science. In the theoretical part of this paper, we firstly show that quantum models can be exponentially more efficient than probabilistic models because there exist datasets that admit low-dimensional quantum models and only exponentially high-dimensional probabilistic models. Secondly, we explain in what sense quantum models realize a useful relaxation of compressed probabilistic models. Thirdly, we show that sparse datasets admit low-dimensional quantum models and finally, we introduce a method to compute hierarchical orderings of properties of users (e.g., personality traits) and items (e.g., genres of movies). In the empirical part of the paper, we evaluate quantum models in item recommendation and observe that the predictive power of quantum-inspired recommender systems can compete with state-of-the-art recommender systems like SVD++ and PureSVD. Furthermore, we make use of the interpretability of quantum models by computing hierarchical orderings of properties of users and items. This work establishes a connection between data science (item recommendation), information theory (communication complexity), mathematical programming (positive semidefinite factorizations) and physics (quantum models).
We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical methods for problems involving low-rank matrices, but with complexity bounds that exhibit a hefty polynomial overhead compared to quantum algorithms. This raised the question of whether these methods were actually useful in practice. We conduct a theoretical analysis aimed at identifying their computational bottlenecks, then implement and benchmark the algorithms on a variety of problems, including applications to portfolio optimization and movie recommendations. On the one hand, our analysis reveals that the performance of these algorithms is better than the theoretical complexity bounds would suggest. On the other hand, their performance as seen in our implementation degrades noticeably as the rank and condition number of the input matrix are increased. Overall, our results indicate that quantum-inspired algorithms can perform well in practice provided that stringent conditions are met: low rank, low condition number, and very large dimension of the input matrix. By contrast, practical datasets are often sparse and high-rank, precisely the type that can be handled by quantum algorithms.
Recommender systems are crucial for customizing user experiences across diverse sectors such as e-commerce and entertainment. Traditional correlation methods have been employed to forecast user preferences; however, they frequently prove inadequate when addressing intricate, high-dimensional datasets. Quantum computing presents a new approach for enhancing correlation computations, potentially resulting in more precise recommendations. This study seeks to address and compare the efficiency of classical and quantum correlation techniques in recommender systems utilizing four distinct datasets: Supermarket Sales, IMDB Top 250 movies, MovieLens 10k, and BigBasket products. The Item Recommendation and Quantum Correlation (IRQC) method, makes use of parameterized quantum circuits with rotation gates and entanglement. The experimental methodology comprised the utilization of both classical and quantum correlation approaches, evaluating their efficacy through critical metrics including mean absolute error (MAE) and root mean squared error (RMSE). The results demonstrated that quantum correlations consistently surpassed classical correlations across all datasets. The proposed Quantum Correlation approach obtains lower mean absolute errors of 0.99, 0.30, 0.90, and 0.92 in BigBasket, Supermarket Sales, IMDB Top 250 Movies, and MovieLens 10K datasets, respectively, than 1.20, 1.48, 1.10, and 1.00 with the classical methods. This study underlines the potential of quantum computing in machine learning applications, notably for boosting recommendation systems.
The rapid growth of ultra-large and highdimensional datasets has intensified the demand for deep learning (DL) models that are scalable, accurate, transparent, and interpretable. In parallel, quantum-inspired computing has emerged as a promising paradigm that emulates quantum principles such as superposition, entanglement, and probabilistic state evolution without requiring quantum hardware. This study presents a comprehensive survey of explainable quantum-inspired DL models for large-scale data mining. Existing quantum-inspired architectures integrated with deep neural networks (DNN), including convolutional, recurrent, and attention-based models, are systematically analyzed alongside explainable artificial intelligence (XAI) techniques to enhance interpretability and trustworthiness. The reviewed methods are classified based on learning paradigms, explainability mechanisms, scalability strategies, and application domains such as healthcare analytics, cybersecurity, intelligent transportation, and industrial big data systems. Furthermore, evaluation metrics, computational complexity, and performance trade-offs are examined in comparison with conventional DL approaches. Finally, key open challenges and future research directions for real-world large-scale deployment are highlighted.
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.
Motivated by recent progress in quantum technologies and in particular quantum software, research and industrial communities have been trying to discover new applications of quantum algorithms such as quantum optimization and machine learning. Regardless of which hardware platform these novel algorithms operate on, whether it is adiabatic or gate based, from theoretical point of view, they are performing drastically better than their classical counterparts. Two promising areas of quantum algorithms quantum machine learning and quantum optimization. These are based on performing matrix operations using quantum states and operation, in order to speed up data analysis where quantum computing can efficiently work with high dimensional vectors. Motivated by that, quantum inspired algorithms (e.g. for recommendation systems and principal component analysis) are developed to cope with high dimensionality using probabilistic techniques that are inspire from quantum computing. In this paper we review recent progress in the area of quantum inspired algorithms for low rank matrix approximation. We further explore the possibility of using parametrized complexity for such algorithms to refine practical complexity analysis. Finally, we conjecture that quantum inspired algorithms that use low rank approximation and also sample and query technique for input representations are Fixed Parameter Tractable (FPT).