Quantum Systems State Estimation And Tracking Control

With the rapid development of information technology in21st century, people’s attention on quantum communication, quantum computing and quantum information continues to increase. More and more people are concerned about the research of quantum communication and continue doing further research. This dissertation is mainly focus on the study of the state estimation and quantum system tracking control. The main research can be divided into following two aspects:1. Comparative study of Quantum State Estimation Algorithm based on Compressive SensingThe dimension of the density matrix increases in exponential growth as the qubits of a quantum system becomes larger, which costs a lot of time and huge computation to estimate the quantum state. By means of compressive sensing theory, the quantum density matrix can be represented as the compression matrix with low-rank characteristics by the projection of orthogonal basis, and the problem of density matrix estimation is changed to solve an optimization problem with the constrict condition of quantum state estimation error, which saves the computational time, and increases the efficiency of quantum state identification.In this dissertation, we designed several groups of experiments on the quantum state estimation algorithm based on compressed sensing in the MATLAB environment. First, we use the alternating direction multiplier algorithm (ADMM) to estimate the density matrix of six qubits. The performance comparisons with the least squares and Dantzig optimization methods are studied with and without external interference. Second, the influence of the increasing qubits on the state estimation is studied by adopting the ADMM algorithm to estimate quantum state under the different qubits. Third, we implement the estimation of seven qubit. Finally, we propose an adaptive parameter value ADMM algorithm to improve the original fixed parameter value ADMM algorithm. The fast estimation of quantum pure state is realized, which shows that the ADMM algorithm is the most effective in three algorithms, which has great advantage in higher quantum qubits state estimation.2. Dynamic Function Tracking Control of Quantum SystemsA time-varying quadratic function is selected as a traget function. The Schrodinger equation of quantum systems is used to study the trajectory tracking. A suitable Lyapunov function is selected based on Lyapunov stability theorem, we design control laws to complete the system to track the target function from any initial state. System simulation experiments and the performances comparisons are studied under different initial states. The simulation results in Matlab environment show the superiority of the control laws on the track of the target function, and by comparing the results of different initial states and observables; we study the effects of initial states to systems tracking performance. Tracking time and control accuracy are improved by further adjusting the system control parameters.