| Quantum entanglement is a critical resource in quantum communication and quantum information processing.Monogamy of entanglement is an essential tool to characterize the inner features of quantum entanglement.Recent years,it has been still unclear to describe the monogamy of entanglement in higher quantum systems,which gradually becomes a hot topic of the moment.On the other hand,the powerful computing ability and decryption ability of quantum computers gradually catch our attention.Compared with classical computation,quantum computation makes use of quantum mechanical properties,such as quantum entanglement,quantum superposition,so that it can have potential advantages when applied to cross-cutting areas.Therefore,the applied research of quantum computing is also important.As for the theoretical researches of quantum entanglement,we choose Rényi-α entropy as the main entanglement measure to investigate the monogamy and polygamy of entanglement for generalized W-class states in higher-dimensional quantum systems,and the related applications are also provided;we also describe tighter entanglement equalities using negativity,entanglement of formation and Rényi-α entropy.As for the applied researches of quantum computing,we try to transform the famous residual learning in classical neural network into quantum concept.Then we design a novel hybrid quantum-classical neural network with deep residual learning,and get the ideal experimental results.Our detailed research results in this thesis are as follows:First,the monogamy and polygamy relations of entanglement for generalized W-class states.As for the generalized W-class states in n-qubit quantum systems,we make use of the existed analytical relations between Rényi-α entanglement and concurrence to investigate the entanglement distribution of n-qubit generalized W-class states with different range ofα;as for the generalized W-class states in n-qudit quantum systems,we derive analytical expression of Rényi-α entanglement and concurrence with respect to arbitrary partition of subsystems,and then using the results,we analyse the monogamy and polygamy relations for n-qudit generalized W-class states.In the application of theoretical research,for the results of n-qubit generalized Wclass states,we consider two quantum states in higher-dimensional quantum systems to test the obtained inequalities;for the results of n-qudit generalized W-class states,we establish two concepts named "partition-dependent residual entanglement(PREs)"to analyse the entanglement dynamics of the generalized W-class states.Taking a 6qubit W state as an example,we explore the relations among the value of PREs,αand all possible partitions of one subsystem,and finally get the full understanding of the entanglement dynamics for 6-qubit W state.For future study,we can also develop a possible comprehensive analysis of the entanglement dynamics in an infinite or finite time using PREs.Moreover,we also apply the results obtained from the n-qudit generalized W-class states into an interesting quantum game,and quantify the difference between classical game and quantum game.Second,tighter monogamy and polygamy relations of entanglement.Recent years,the monogamy and polygamy inequality of multiqubit quantum entanglement have been a hot topic for research.The results involve many kinds of entanglement measures,such as concurrence,negativity,Rényi-α entropy and Tsallis-q entropy.We find out that designing efficient analytical mathematical inequalities can tight the existed monogamy and polygamy inequalities.Tighter monogamy and polygamy relations imply finer characterizations of the entanglement distribution.Finally,a hybrid quantum-classical neural network with deep residual learning.In classical neural networks,deeper network has higher training errors and testing errors with increased depth,which is called the degradation problem.In 2016,deep residual learning was proposed to improve the degradation problem,and achieved the experimental success.This leads us to consider whether we can take this efficient residual learning into quantum neural networks.So we firstly define the structure of residual learning in quantum neural networks,and design a novel hybrid quantum-classical neural network with deep residual learning(Res-HQCNN).We also present an effective training algorithm.As far as we know,no work has been attempted up to now.In order to test the validity of Res-HQCNN,experiments for noisy and non-noisy quantum data are carried out on a classical computer.Compared with the quantum neural network without residual learning,experimental results show that Res-HQCNN can learn an unknown unitary operator better when the quantum data is noise free;Res-HQCNN is more robust to noisy data when quantum data is noisy.In addition,we also discuss another method to define the residual structure in quantum concept as a reference for readers. |
