Classification Algorithms And Application Research Based On Quantum Machine Learning

Quantum computing has advantages over classical computing in terms of computational speed and computational power,which can be applied to tackle some challenging problems in machine learning,providing new ideas and methods to enhance the performance of classical machine learning algorithms.Quantum machine learning is the utilization of quantum devices to implement machine learning algorithms.Variational quantum algorithms are an important class of quantum machine learning algorithms that can be used to solve various machine learning tasks.Quantum neural networks can be seen as a type of implementation of variational quantum algorithms,and they have attracted a lot of attention in the era of noisy intermediate-scale quantum.Classification tasks often involve processing large volumes of data,and quantum computers have the potential to offer faster and more efficient processing for such tasks.Therefore,utilizing quantum neural networks to address classification problems is a highly reasonable choice.Theoretical foundations for quantum neural networks are not yet well understood despite extensive research into their practical applications.In this thesis,we focus on developing a theoretical framework for data re-uploading quantum neural networks,which consist of interleaved trainable block and encoding block.Our work provides a rigorous characterization of the expressive power of the single-qubit quantum neural network model.We demonstrate that this model can approximate any univariate function by mapping the model to a partial Fourier series.In particular,we establish exact correlations between the trainable parameters and coefficients of the Fourier series,resolving a previously open problem on the universal approximation property of quantum neural networks.We also analyze the limitations of the single-qubit native quantum neural networks in approximating multivariable functions from the perspective of the multivariate Fourier series and propose an extension scheme for a multi-qubit model.Furthermore,we conduct numerical experiments on the Baidu Paddle Quantum simulation platform to demonstrate the expressive power and limitations of the single-qubit native quantum neural network.Additionally,we perform classification experiments on multiple datasets and observe good classification performance and practicality in such quantum neural networks.In order to further investigate the performance of the model in handling classification problems,we introduce two quantum siamese neural network models.One of the models utilizes a classical neural network as the main body of the siamese network and employs our proposed multi-qubit quantum model for similarity metrics,while the other model uses a quantum neural network as the main body of the siamese network and applies a fully connected neural network for post-processing.We then perform simulation experiments on actual datasets using these two schemes.The experimental results reveal that both models exhibit good performance in various test tasks.Nevertheless,a comparative analysis of the results and embeddings indicate that the scheme with the classical network as the main body of the model achieves better performance.