In the era of big data, traditional regression models cannot deal with uncertain big data efficiently and accurately. In order to make up for this deficiency, this paper proposes a quantum fuzzy regression model, which uses fuzzy theory to describe the uncertainty in big data sets and uses quantum computing to exponentially improve the efficiency of data set preprocessing and parameter estimation. In this paper, data envelopment analysis (DEA) is used to calculate the degree of importance of each data point. Meanwhile, Harrow, Hassidim and Lloyd (HHL) algorithm and quantum swap circuits are used to improve the efficiency of high-dimensional data matrix calculation. The application of the quantum fuzzy regression model to small-scale financial data proves that its accuracy is greatly improved compared with the quantum regression model. Moreover, due to the introduction of quantum computing, the speed of dealing with high-dimensional data matrix has an exponential improvement compared with the fuzzy regression model. The quantum fuzzy regression model proposed in this paper combines the advantages of fuzzy theory and quantum computing which can efficiently calculate high-dimensional data matrix and complete parameter estimation using quantum computing while retaining the uncertainty in big data. Thus, it is a new model for efficient and accurate big data processing in uncertain environments.
In the era of big data, traditional regression models cannot deal with uncertain big data efficiently and accurately. In order to make up for this deficiency, this paper proposes a quantum fuzzy regression model, which uses fuzzy theory to describe the uncertainty in big data sets and uses quantum computing to exponentially improve the efficiency of data set preprocessing and parameter estimation. In this paper, data envelopment analysis (DEA) is used to calculate the degree of importance of each data point. Meanwhile, Harrow, Hassidim and Lloyd (HHL) algorithm and quantum swap circuits are used to improve the efficiency of high-dimensional data matrix calculation. The application of the quantum fuzzy regression model to small-scale financial data proves that its accuracy is greatly improved compared with the quantum regression model. Moreover, due to the introduction of quantum computing, the speed of dealing with high-dimensional data matrix has an exponential improvement compared with the fuzzy regression model. The quantum fuzzy regression model proposed in this paper combines the advantages of fuzzy theory and quantum computing which can efficiently calculate high-dimensional data matrix and complete parameter estimation using quantum computing while retaining the uncertainty in big data. Thus, it is a new model for efficient and accurate big data processing in uncertain environments.
In the objective world, how to deal with the complexity and uncertainty of big data efficiently and accurately has become the premise and key to machine learning. Fuzzy support vector machine (FSVM) not only deals with the classification problems for training samples with fuzzy information, but also assigns a fuzzy membership degree to each training sample, allowing different training samples to contribute differently in predicting an optimal hyperplane to separate two classes with maximum margin, reducing the effect of outliers and noise, Quantum computing has super parallel computing capabilities and holds the promise of faster algorithmic processing of data. However, FSVM and quantum computing are incapable of dealing with the complexity and uncertainty of big data in an efficient and accurate manner. This paper research and propose an efficient and accurate quantum fuzzy support vector machine (QFSVM) algorithm based on the fact that quantum computing can efficiently process large amounts of data and FSVM is easy to deal with the complexity and uncertainty problems. The central idea of the proposed algorithm is to use the quantum algorithm for solving linear systems of equations (HHL algorithm) and the least-squares method to solve the quadratic programming problem in the FSVM. The proposed algorithm can determine whether a sample belongs to the positive or negative class while also achieving a good generalization performance. Furthermore, this paper applies QFSVM to handwritten character recognition and demonstrates that QFSVM can be run on quantum computers, and achieve accurate classification of handwritten characters. When compared to FSVM, QFSVM’s computational complexity decreases exponentially with the number of training samples.
Neural network is one of the AI algorithms commonly used to process data, and has an extremely important position in scenarios such as image recognition, classification, and machine translation. With the increase of data volume explosion, the required computing power of neural networks is also significantly increased. The emergence of quantum neural networks improves the computational power of neural networks, but the accuracy of neural networks and quantum neural networks is not high in the face of the complexity and uncertainty of big data. In order to improve the efficiency and accuracy, the cross-fusion of "fuzzy number theory + quantum neural network" is proposed to study the quantum fuzzy neural network (FQNN) based on fuzzy number. The Gaussian fuzzy function is used to generate the corresponding fuzzy affiliation matrix to describe the uncertain information in the data. The fuzzy independent variables are trained through the FQNN model, and the model is output after changing the parameters of the quantum forward propagation layer. Simulation experiments show that the quantum fuzzy neural network model based on fuzzy number is more efficient and accurate in this study compared with the quantum neural network model.
A financial market is a trading system for financial assets such as derivatives, stocks, currencies, and bonds. Financial markets, which can be virtual or physical, are essential to the world economy. Financial forecasting has become an enormous difficulty due to the markets’ quick internationalization and the volume of data gathered from various sources growing at an accelerating rate. The study explores the creation of a model for stock market forecasting that leverages the power of big data analytics and quantum computing (QC). By handling multifaceted datasets and achieving high-accuracy forecasting, big data and QC improve market trends and insights. This is achieved by leveraging QC speed-driven problem-solving capabilities. In this study, we proposed a novel Hippopotamus Optimized Quantum Refined Support Vector Machine (HO-QRSVM) to predict the financial market. The financial dataset came from several places, such as economic databases and stock exchanges. The preprocessed data from the acquired data were cleaned and normalized. To remove dimensionality and extract features from preprocessed data, principle component analysis (PCA) is used. The capacity of QC to handle entanglement and superposition enables the simultaneous investigation of several potential market situations, leading to faster convergence and more precise forecasts. The result demonstrated the proposed method has significant improvements in prediction accuracy compared to other traditional algorithms. The performance evaluation techniques include the F1-score (96.3%), recall (98.2%), accuracy (98.5%), and precision (98.3%). The research, big data analytics, and QC combined can greatly improve financial market forecasts, giving decision-makers and strategic investors an advantage over their competition.
Climate change is accelerating, necessitating sophisticated forecasting techniques to alleviate its impacts efficiently. The huge amount and diversity of climate data frequently exceed the endurance of traditional computing techniques, creating problems with accuracy and processing speed. This research presents a quantum-enhanced framework for big data analytics in climate science by combining quantum machine learning, optimisation, and simulation methods. The recommended strategy empowers specific analysis of high-dimensional climate datasets, contributing noteworthy enhancements in predicting critical phenomena such as temperature irregularities, rainfall trends, and catastrophic weather patterns. By including quantum algorithms, the framework attains scalability and real-time competencies, minimising computational processing times while improving predictive accuracy. These results demonstrate the advantage of quantum-enhanced models over classical approaches by giving innovative tools for policymakers and industry leaders to help them make data-driven, well-informed decisions. The study highlights the revolutionary potential of quantum computing in addressing global climate challenges, making new paths for environmentally friendly remedies. As quantum technologies develop, their use in climate science will motivate innovative solutions for the endurance and preservation of the environment. Major Findings: This study highlights the necessity for cross-disciplinary collaboration to completely integrate quantum computing advancements into climate modelling, guaranteeing actionable and accurate perceptions. The results show how important quantum-enhanced analytics can be in helping to develop sustainable decision-making to deal with the escalating climate crisis.
Low-rank matrix regression is a pivotal technique in image processing and pattern recognition that can directly handle data with intrinsic matrix structures. However, classical algorithms for this task suffer from a computational bottleneck, where the complexity escalates cubically with the matrix dimension, incurring prohibitive costs for high-dimensional datasets. In this study, we propose a quantum algorithm for low-rank matrix regression with feature extraction, leveraging the Harrow–Hassidim–Lloyd algorithm for regression matrix estimation and a modified quantum singular-value thresholding algorithm for iterative variable updates. Theoretical analysis demonstrates that our algorithm reduces the time complexity dependence on the matrix dimension from cubic to logarithmic, achieving an exponential speedup over classical counterparts when the problem is well conditioned and the precision requirements are moderate. Furthermore, we introduce an algorithmic variant utilizing the quantum memory model to bypass the reliance on quantum random access memory. Additionally, we propose a hybrid strategy leveraging quantum sketching techniques to effectively eliminate the runtime dependence on the condition number. Subsequently, we performed small-scale quantum experiments to validate the feasibility of our proposed quantum algorithm.
Quantum computing, with its unique parallel computing ability and efficient optimization algorithm, provides new possibilities for the optimization of complex systems. This paper aims to explore the modeling and optimization methods of complex industrial engineering systems based on quantum computing and big data analysis technology. Through the comprehensive application of quantum approximate optimization algorithm, quantum support vector machine, data mining and machine learning technology, this study has realized the accurate modeling and optimization of complex industrial engineering systems. The research results show that compared with the traditional ID3 algorithm, the method adopted in this study shows better real-time performance and smaller relative error in industrial system assessment, which significantly improves the accuracy of assessment. This achievement not only provides more reliable data support for the prediction and risk control of industrial systems, but also verifies the effectiveness of quantum computing and big data analysis in dealing with complex system modeling and optimization problems. To sum up, the method proposed in this paper is expected to bring sustainable development momentum to the field of industrial engineering, and improve the decision-making support ability and risk control level of enterprises.