Multipartite Entangled State And Quantum Machine Learning

Quantum information,as an intersecting frontier field of quantum mechanics and informatics,has attracted great interest from researchers.By introducing the unique entanglement and coherence characteristics of quantum systems into traditional infor-matics,people have broken many original inherent cognitions and demonstrated the quantum supremacy in many research directions.This thesis starts from three small directions,showing the application of entanglement resources in quantum information and the advantages it brings.In the first part,we mainly review some basic concepts and knowledge in quantum information,including the most basic knowledge in quantum computing such as qubits,quantum gates,and quantum measurement,which will be the third part of quantum machines.In addition,the quantum Fisher information is introduced,which provides a basic concept for the subsequent part of the fourth part of quantum metrology.In the second part,we introduce the experiment of realizing a quantum generative adversarial network in a programmable superconducting quantum chip,where the gen-erator and discriminator are both parameterized quantum circuits composed of single-qubit rotating gates and multi-qubit entanglement gates.And we also use the Hadamard test method to measure the gradient of parameters.In the experiment,we successfully replicated a classic XOR gate through alternate training of the generator and the dis-criminator,and the average fidelity of 4 different output states reached 0.927.This experiment shows that quantum neural networks based on superconducting quantum cores have nonlinear representation and good scalability.In the third part,we introduce a quantum metrology scheme,which measures the magnetic susceptibility of the atomic spin ensemble along theanddirections,and estimates the parameters with precision beyond the standard quantum limit.In our scheme,to estimate one parameteronly requires two single-shot measurements along the directions ofand.After many（approximately 1000 times）numerical simu-lations,and the scale of the uncertainty relative to the number of atomic spinsis（1.43±0.02）/N^0.687±0.003.In the fourth part,we study the ground state diagonal entropy of quantum many-body systems,including the XY model and the Ising model with next-nearest neighbor interaction.Research has shown that,regardless of whether the model is integrable or not,the diagonal entropy in a many-body system can be expressed as a volume term plus logarithmic correction and constant terms.The critical point can be judged by the three coefficients of diagonal entropy.