Research On Quantum Machine Learning Model And Realization Of Quantum Circuit

Quantum machine learning is an interdisciplinary research direction that combines quantum computing and machine learning.The classic machine learning algorithms have achieved excellent results in many fields such as pattern recognition,image classification,and temporal series prediction.But with the advent of the era of data explosion,machine learning algorithms require stronger and stronger computing power.In recent years,classical computers have been closed to the theoretical limits of physics,forcing researchers to search for potential physical platforms and algorithms which have large-scale information processing capabilities.Quantum computers are one of the most promising directions for realizing our demands.Thanks to the superposition and entanglement of quantum,quantum computers possess the unique parallel characteristic.Compared with classical computers,quantum computers have enormous potential information processing capabilities,in some unique fields.In order to take full advantage of quantum computers,quantum algorithms need to be designed.This paper revolves around machine learning models,provides quantum algorithms for their important steps,and constructs scalable quantum circuits that can be deployed on real quantum devices.According to different basic frameworks,our main work can be divided into two categories:(1)Based on the classical machine learning framework,quantum counterparts of the sub-steps with high complexity(for example,searching the maximum/minimum,calculating the inner product)are proposed,in order to reduce the computational complexity of these sub-steps,thereby accelerating the entire machine learning model.(2)Based on one of the mainstream quantum machine learning frameworks,parameterized quantum circuits,quantum algorithms for the steps commonly used in machine learning models are designed,in order to achieve the goal that the entire model can be deployed on quantum computers.Specifically,the main work of this paper can be summarized as follows:1.Solving maximum/minimum is an indispensable step in machine learning models.However,the high failure probability of the current quantum algorithm limits its effectiveness.Based on sample estimation and probability statistics,our paper proposes an improved algorithm,which can effectively reduce the failure probability,thereby reducing the number of quantum algorithm iterations,thereby reducing the number of quantum initial state preparations.Compared with the current quantum algorithm,our algorithm reduces the required number of quantum initial state preparations from O((log2 N)2)to 0(log2 N),while maintaining the complexity of O((?)),where N is the database size.And we design and optimize scalable quantum circuits for improved quantum algorithms and successfully deploy them on IBM’s superconducting quantum computers.2.With the development of neuroscience,neural network models,as an important part of machine learning,are widely used in various fields,and the main computational complexity of neural networks lies in massive and high-dimensional vector inner product operations.However,the current quantum algorithm is still not ideal for high-precision inner product operations.Based on quantum phase estimation and swap-test,our paper proposes an improved quantum algorithm for calculating the inner product of vectors,and designs a scalable quantum circuit for it.We theoretically derive the algorithm complexity,computational accuracy and minimum success probability,and further improve this minimum success probability by relaxing the conditions.Specifically.The complexity of our algorithm is O(log2 ε-1×log2 N),while the complexity of the classical algorithm and the current quantum algorithm is O(N)and O(ε-2 log2 N),respectively.In numerical simulations,we embed the improved quantum algorithm of the unsigned vector inner product into a fully connected neural network(Perceptron)and a spiking neural network(Tempotron).The results show that neural networks embedded with the quantum algorithm have the same classification accuracy as the models running on a classical computer.3.Except for the inner product operation,the convolution operation also frequently appears in neural network models.Based on the parameterized quantum circuit framework,our paper designs aquantum graph convolutional layers(QGCL)for node classification tasks and topological graph classification tasks,respectively.Quantum circuits of QGCL consist of a fixed quantum circuit corresponding to the adjacent matrix and an adjustable quantum circuit that replaces the weight matrix.We propose a quantum Karnaugh map(QKM)to solve the mapping problem between arbitrary adjacent matrices and their corresponding quantum circuits,and treat a series of quantum phase gates as adjustable quantum circuits,where the phases are adjustable parameters.We theoretically deduce that in the case of regular topological graphs,the basic quantum gate complexity of a QGCL is 0(s2(log2 N)3),while the complexity of its classical counterpart requires O(sN)multiplications operation,where N is the total number of nodes or the size of the input data,s is the number of neighbor nodes of each nodes or the size of the convolution kernel.When the number of neighbor nodes of each node in the topological graph is much smaller than the total number of nodes in the topology graph,the QGCL has an exponential acceleration advantage,compared with its classical counterpart.The simulation experiment of QGCL shows that it can achieve the same accuracy as its classical counterpart in node classification and topology map classification tasks,and QGCL has a fewer number of parameters and lower complexity.The experiment of using QKM to generate quantum circuits for random permutation matrices with different scales shows that QKM has high-efficiency and scalability.