Measurement,State Estimation And Control In Quantum Systems

Quantum measurement is the most important way for people to obtain quantum information,and it is also one of the foundations of quantum mechanics.After the measured data needs to be evaluated by quantum state,people can get the overall knowledge of the quantum state.Therefore,quantum measurement and state estimation are particularly important in the fields of quantum information and quantum control.In this dissertation,the quantum measurement and quantum state estimation are fully and deeply studied.Based on this,the various techniques of quantum measurement and its effects on the system control are emphasized,and various methods and practical applications of quantum state estimation are studied.And measurement-based real-time quantum state estimation and control.1.Based on the principle of nuclear magnetic resonance(NMR)measurement,compressed sensing theory(CS)and its optimization algorithm,a fast method for the NMR quantum state estimation is proposed and applied to practical NMR quantum experiments.According to the actual measurement operator and the grouping of measurement data in the actual NMR experiment,a measurement data sampling strategy based on the group is proposed,and it is proved that the convex state optimization equation of the quantum state estimation established under this strategy has the unique optimal solution.Combining with CS theory,it is proved that when the measured data is far less than the complete data,the optimal solution of the convex optimization equation still has a maximum probability equal to the density matrix of the actual NMR quantum state.The proposed method was used to estimate the state of spin states of 2,3,and 4 bits in the actual NMR solution.Finally,according to different optimization algorithms and the results of quantum state estimation under different measurement sampling rates,the experimental performance is compared and analyzed.2.Propose and prove the minimum number of measurements required for accurate estimation of any quantum pure state,and give the corresponding construction method of the optimal measurement operator set.According to the characteristics of the quantum measurement mechanics operator and the state density matrix,a two-step measurement method based on self-adaptation is proposed.For an arbitrary n-qubit quantum pure state,an optimal operator can be constructed by using the proposed 2n 2l-3 operator.The symbol set,based on the measurement operator and the corresponding measurement result in the set,constructs and solves the optimization equation to obtain an accurate estimate of the density matrix of the pure state,where l is the number of non-zero eigenvalues of the density matrix.We theoretically prove that 2n +2l-3 is the minimum number of times required for accurate estimation of the pure state.Finally,the proposed method of construction and estimation is applied to the estimation of the actual state of the NMR experiment,and the comparison between the experimental verification and the characteristics is performed.3.Based on a series of discrete projection measurements,the optimal measurement of eigenstates and superposition states in a closed two-level quantum system is achieved.By applying discrete projection measurements,the state of the system can be adjusted to the target state.The formula of the relationship between the control fidelity and the selected measurement operator is given.By taking the fidelity maximum value,the corresponding measurement operator is selected to achieve the optimal measurement and control with minimum global decoherence.The optimal measurement and control were applied in the three cases of interaction picture,Schrodinger picture and the presence of additional control field,and the characteristics were analyzed through comparative experiments.Finally,the feasibility of the optimal measurement and control in the actual system is analyzed.4.Real-time estimation of the state of a two-level quantum system based on continuous weak measurements.The system dynamics evolution equation based on weak measurement principle is given to obtain real-time measurement data.Using the method of painting transformation,the influence of the evolution of the quantum state on the state is converted to the evolution of the measurement operator,so that the measurement values at different moments are converted into measurement data for the state at the same moment.Based on the theory of compressed sensing,a real-time estimation of the state is obtained by solving a state optimization equation.Finally,the proposed real-time estimation scheme was verified by simulation experiments,and the characteristics were compared and analyzed.