Researches On Quantum Measurement And Estimation In Circuit QED

Superconducting circuit QED has been regarded as a promising candidate for the realization of quantum computing because of its scalability and controllability.This thesis introduces the composition of the linear circuit QED which uses a linear resonator and the evolution of the qubit in it.Considering the nonlinear circuit QED which uses a nonlinear resonator,the conditions under which the device will exhibit bistability and the influence of introducing the nonlinear resonator are discussed.Based on the linear circuit QED,this thesis theoretical studies the quantum Bayesian approach that completes the task of real-time monitoring the system states and analyzes its suitable conditions.Finally,this thesis proposes a measure for the degree of non-commuting behavior of quantum measurements,and demonstrates its rationality and effectiveness.The main contents of this thesis are as follows:Firstly,this thesis mainly introduces the recent developments of quantum state tomography,which consist of quantum state tomography based on quantum continuous weak measurement and maximum-likelihood estimation,quantum state tomography based on compressive sensing,and quantum state tomography based on linear regression estimation.Their scope of application as well as the respective advantages and disadvantages has been analyzed in addition.Considering the linear circuit QED system,the composition of the system and the evolution of the qubit are introduced.Moreover,the nonlinear circuit QED system that uses a nonlinear resonator is considered.The conditions under which the device will exhibit bistability are obtained by analizing the steady-state equation of the amplitude of the cavity field.Through applying a displacement transformation on the system and tracing over the cavity state,the effective stochastic master equation for the qubit in the nonlinear circuit QED can be obtained,which is compared to the one in the linear system to analyze the influence of introducing the nonlinear resonator on the evolution of the qubit.Based on the linear circuit QED,this thesis theoretically studies the quantum Bayesian approach.The process and theory of the quantum Bayesian approach are introduced,its effectiveness is proved through numerical simulation.Suitable conditions under which the quantum Bayesian approach can accurately update the density matrix of the qubit are analyzed through considering the correlation between some basic and physically meaningful parameters of the circuit QED and the performance of the Bayesian approach.Our results advance the understanding of the quantum Bayesian approach.Finally,we de ne a measure for the degree of non-commuting behavior of quantum measurements coming from the initial and nal states of the measurements,Considering the simultaneous measurement of non-commuting observables.The rationality of our measure is demonstrated and the application of it is presented.Our work deepens the understanding of quantum non-commuting measurement.