Research On Parameter Estimation Algorithm And Precision Optimization In Open Quantum Systems

The second quantum revolution is now ready to be enabled.Presently,a huge amount of research interest has been attracted on the fields of quantum computing and quantum commu-nication.While an important premise of quantum computing and quantum communication is to accurately obtain the internal parameters of quantum system in order to achieve the purpose of controlling the quantum system.Quantum parameter estimation is exactly a subject related to measuring and statistical inferencing for physical quantities in quantum systems,with its core topic being to obtain high-precision estimates of unknown physical quantities by using measured data.The results of quantum estimation have been widely applied to the fields for quantum gyroscopes,quantum frequency standards,and gravitational wave detection.Quan-tum parameter estimation is not only an inevitable product of technological progress,but also feeds back into promoting the modern physics.This thesis studies the parameter estimation of an unknown quantity and its associated ac-curacy limit in both continuous weak-measurement based quantum systems and optomechanical systems,respectively.In terms of estimation accuracy,a numerical method of computing the Fisher information is proposed for the estimation problem of any internal parameter in an open quantum system with continuous weak measurement.In terms of value estimation,a method of using hypothesis testing to rapidly select an optimal value,which is the closest to the true value from the candidate values is proposed,on the basis of quantum measurement data.In addition,a real-time unbiased estimation to the time-varying external force of a class of optomechani-cal systems is provided under measuring the optical field.The main research contents are as follows:1)A numerical computing method for Fisher information.This thesis first constructs a continuous weak-measurement based quantum system for parameter estimation.On this ba-sis,a new algorithm for numerically calculating Fisher information is proposed according to the Metropolis Hastings algorithm and the Makov Chain Monte Carlo integration.This algo-rithm can be used to further optimize the estimation accuracy by selecting various measurement schemes.Based on the proposed algorithm,the influenced of different measurement operators and measurement efficiencies on Fisher information are discussed.It is worth noting that this algorithm can be extended to the numerical computing of the single parameter estimation accu-racy in a d-dimensional open quantum system.2)Efficient value discrimination in parameter estimation.A weak-measurement based open quantum system is constructed for parameter estimation.With a priori knowledge about the candidate values of the parameter to be estimated,a value discrimination method for ef-ficiently estimating the parameter is proposed based on the measurement.The evolution of the posterior probability of each hypothesis in the hypothesis testing is derived by Bayesian inference and making use of the master equation and measurement output.Based on the pro-posed Bayesian criterion,the average error probability is provided as an index to quantify the distinguishing effect of the hypothesis testing.The feasibility of the proposed hypothe-sis testing method in value discrimination is verified in estimating an unknown Hamiltonian in a two-dimensional superconducting qubit.Meanwhile,the efficiency of the proposed method is demonstrated by comparing the computing times of the average error probabilities under the maximum a posteriori criterion and the Bayesian criterion.3)Real-time external force estimation in optomechanical systems.Based on the Hamilto-nian of cavity optomechanical system,the quantum Langevin equation of the dynamic evolution of the system is derived.The evolution of the optical model is eliminated through weak coupling such that the output equation of the optical field is obtained.As a result,the evolution of the system together with the measurement output can be described by a linear Gaussian stochastic equation.Then the estimation of the time-varying external force of the cavity optomechanical system is converted into the input estimation of the linear Gaussian system,and the unbiased minimum variance Kalman filter can be used to obtain the unbiased estimate of the system state.Based on the relationship between the system state and the external force,the unbiased estimate of the time-varying external force and the corresponding estimation accuracy are derived.The effectiveness of the proposed algorithm is verified by Monte Carlo experiment and the influence of temperature on numerical accuracy is also discussed.