Research On Key Issues And Algorithms Of Quantum Machine Learning

As one of the mainstream technologies in artificial intelligence,machine learning has achieved great success and profound impact in many fields thanks to the rapid development of high-performance computing hardware.However,with the gradual invalidation of Moore’s Law,the speed and performance of classical von Neumann computers will face bottlenecks.How to improve the existing computing power to realize machine learning tasks more efficiently has become an urgent problem to be solved.In addition,with the advancement of a new round of information technology revolution,the explosive growth of data volume also indirectly exacerbates the urgency of this task.On the other hand,due to the unique properties of quantum superposition and entanglement,quantum computing has shown the potential to surpass classical computing and has received extensive attention and research in recent years.Quantum machine learning is an emerging discipline that integrates quantum computing and machine learning.It aims to use the advantages of quantum computing to provide acceleration or performance improvement for classical machine learning algorithms.Although quantum machine learning shows broad development prospects and is expected to bring a new round of technological innovation,it is still in its infancy as a whole,and there are still some key challenges.In this context,this paper conducts further research and proposes corresponding solutions for several key problems in the current field of quantum machine learning.At the same time,focusing on typical machine learning tasks such as feature selection,data dimensionality reduction,unsupervised clustering,and supervised classification,quantum extensions with accelerated advantages or better performance compared with classical machine learning algorithms have been developed.The specific research contents are as follows:(1)Quantum Feature SelectionBased on the framework of quantum approximate optimization algorithms,three graph theory feature selection algorithms for recent quantum computing devices are proposed.The corresponding graph theory problems are minimum cut,k densest subgraph,and maximum independent set/minimum vertex cover.In addition,further combining the proposed algorithm with tabu search can significantly reduce the consumption of qubit resources,providing a solution to perform largescale feature selection tasks using existing quantum computing devices.Numerical experiments on twenty public datasets show that each quantum feature selection algorithm outperforms the classical scheme.The complexity analysis shows that even in the worst case,the complexity of each algorithm is only O(pn2),where p is the level of the quantum circuit and n is the number of features.(2)Quantum Dimensionality ReductionUsing the idea that the truncated Taylor expansion can be used for function approximation,the quantum state preparation method of the nuclear matrix and the Hamiltonian simulation technology are proposed.On this basis,the existing quantum principal component analysis algorithm is improved,and the quantum kernel principal component analysis algorithm is further designed,which can achieve nonlinear dimensionality reduction of quantum data while maintaining quantum acceleration.More importantly,it provides a new solution to the common problem of low nonlinearity in current quantum machine learning models.Furthermore,based on the mathematical correlation of kernel principal component analysis with other nonlinear dimensionality reduction methods,potential schemes for quantum kernel discriminant analysis and quantum manifold learning are explored.(3)Quantum Unsupervised ClusteringA quantum low-rank subspace clustering algorithm is proposed,which consists of two sub-algorithms,quantum low-rank representation,and quantum spectral clustering.Among them,the former designed a quantum algorithm to effectively construct the affinity matrix between samples;the latter designed quantum algorithms to effectively construct the degree matrix,the Laplacian matrix,and the projected Laplacian matrix,respectively,and combined with the quantum k mean clustering algorithm,and finally output the clustering result.Notably,due to the lowrank property of the affinity matrix,the proposed algorithm can naturally circumvent the low-rank assumption of the data in quantum machine learning algorithms.Complexity analysis shows that quantum low-rank subspace clustering has the advantage of exponential speedup compared to classical methods.(4)Quantum Supervised ClassificationA quantum convolutional neural network model for image classification tasks is proposed,which consists of a set of consecutive quantum convolutional layers and a quantum classification layer.This model makes full use of the advantages of quantum superposition and adopts the method of qubit multiplexing,which reduces the consumption of qubit resources to a certain extent.At the same time,the quantum decoherence problem that may be caused by intermediate measurement operations in the previous scheme is avoided.Numerical experiments on two public image datasets show that the proposed model outperforms two previous quantum classifier models.The complexity analysis shows that the proposed model has the advantage of exponential speedup compared with the classical convolutional neural network of the same structure.The research content of this paper will provide new reference ideas and new methods to solve the existing difficulties for the theoretical and applied research of quantum machine learning,which has a certain guiding significance.