The Application Of Lyapunov Control Method For State Transfer In Semiconductor Quantum Dots

Quantum computing is one of the most popular research topics over the world in recent years. Multi-qubits manipulation is the greatest challenge on the way to quantum computing. Semiconductor quantum dot is one of the most popular physical systems for the the qubit manipulation in laboratory. The great integrated technologies and good scalability of semiconductor inspire the researchers to work hard on the manipulation of qubit in semiconductor quantum dots. The LZS(Landau-Zener-Stucklberge) interference has served as a textbook for the qubit transfer in quantum system in recent years. Lots of physicists have worked out the control laws in the experiments based on LZS interference method. In system control theory, the control scheme based on Lyapunov stability theorem has been widely used in the preparation and manipulation of the quantum system, such as superposition states preparation, trajectory tracking and state transfer.In this dissertation, the Lyapunov based control method is applied to the semiconductor quantum dots. The control law specific for the quantum dot system and the pulse generator is designed. The physically realizable control law is verified by system simulation. High performance of the qubit transfer is obtained. Two of the main research contents are as follows:1. Ultra-fast manipulation of the two-level double quantum dots based on Lyapunov control method. The physical system and the Hamiltonian of the quantum dots are studied. The evolution law of the system is obtained based on the Markov master equation. The control law for the double quantum dots is designed via Lyapunov control method. The performance of the state transfer is verified by system simulation. The state transfer probability based on Lyapunov control method is compared to that based on LZS interference method. The conclusion can be draw that:the qubit transfer probability for the initial state|R> to the desired state|L> based on Lyapunov conrol method can be up to99%, which has great advantage over the67%based on LZS interference method; the control process of Lyapunov costs only～50ps, which is much less than that of the LZS interference method.2. Physically realizable control scheme based on Lyapunov control method. As the preliminary control law based on Lyapunov control method is out the scope of current semiconductor quantum dots system and the pulse generator, some improvements of the control law need to be done. The quantum dots system and the KPP (key performance parameter) of the pulse generator are studied deeply. The desired form of the control law is earmarked, and the theoretical improvement work on the Lyapunov control method is performed. The effectiveness of the improved control law is studied by system simulation. The qubit state transfer probability is compared wtih that based on LZS interference. By the system simulation, the conclusion can be draw that:the control performance of the Lyapunov control method has great advantage over that of the LZS interference. The system simulation results show that the improved control law is in the scope of Agilent81134A pulse generator (rise time-75ps) and the Tektronix AWG70000A pulse generator (rise time-20ps), the qubit transfer probability can reach85%and96%, respectively. The fidelity of the control process can be up94%.