Research On Quantum Algorithm For Several Prediction Methods

Prediction algorithm is to find the important information hidden in a large amount of existing data,aiming to realize a better predictive output for a new input data.Due to the rapid development of information technology and the exponential growth of data,traditional forecasting algorithms face major challenges in computing performance when processing existing data.Quantum computing has a significant speed advantage over classical computing in solving some specific problems due to quantum information has superposition,entanglement and other characteristics.Therefore,many researchers combine quantum computing with classical algorithms to provide a new way to solve the problem of high computing time complexity,which result in the quantum algorithm.In this context,this thesis uses the theory,thinking and skills of quantum computing to design some innovative quantum prediction algorithms to efficiently complete the prediction task.The specific work of this study includes:1.Quantum ridge regression algorithm based on HHL framework.The first algorithm presents the quantum state form of the output formula,which can obtain the ideal output value corresponding to the new input data.The second algorithm computes the ideal output value of the whole data set in parallel,and then compares it with the real value of the data set to get the more appropriate regularization parameter value.Compared with the best classical ridge regression,this algorithm has exponential acceleration.2.Quantum vision tracking algorithm based on block coding.This algorithm is an application of quantum prediction algorithm based on ridge regression.The algorithm includes two processes: training process and detection process.In the training process,a ridge regression classifier with quantum state output is trained to obtain the optimal fitting parameters;In the detection process,the optimal fitting parameter classifier obtained in the training process is directly operated,and the output results of new input data are obtained by block coding technology.The whole algorithm achieves exponential acceleration compared with classical visual tracking.3.Quantum gaussian regression algorithm based on HHL framework.In this algorithm,the encoding process of input data is firstly proposed,and the covariance matrix is calculated by annihilation operator and production operator.Meanwhile,a new method is proposed to obtain kernel function vector instead of block encoding method.Next,a quantum gaussian regression algorithm is proposed to calculate the formula of mean and covariance values,which can predict the new input data.This algorithm has quadratic acceleration relative to classical gaussian regression.4.Quantum recommendation algorithm based on Hamming distance.In this thesis,quantum Hamming distance is utilized to propose a quantum recommendation algorithm based on content.In the proposed algorithm,quantum mechanical properties are utilized to sum up the historical movies’ attributes parallelly.In this way,the favorite attributes of the users can be calculated efficiently.Then,from the above result,the quantum Hamming distance between new movies’ attributes and the favorite attributes is derived,which represents the similarity of them.Finally,one new movie with the highest similarity is obtained,which means the task of recommendation is achieved.Moreover,a brief analysis is given,which shows that our algorithm is exponentially faster in the runtime than the classical counterpart.The research in this thesis shows that the prediction task can be realized effectively by using quantum mechanics and properties,and the four quantum algorithms presented in this thesis all have a certain speed advantage,it provides an efficient solution to the challenge of exponential data information in the era of big data.In addition,the research results of this thesis can also provide reference for the design of other quantum intelligent algorithms.