Theory And Simulation Of Semiconductor Quantum Dots System

Quantum computing is an important topic in the field of modern physics, the semiconductor quantum dots is one of the major physical implementations of quan-tum computing. This thesis presents theoretical and simulation studies to address some key problems in the field of the operation and measurement in semiconductor quantum dots, mainly studies two aspects:First, how to design quantum dots to make them bet-ter, which including the device simulation of semiconductor quantum dots, as well as the analysis of decoherence in quantum dots. Second, what can quantum dots be used to do, including achieved ultra-fast universal quantum logic gate with Landau-Zener-Stiickelberg interference, and simulated Kibble-Zurek mechanism(which describes the non-equilibrium phase transition) with Landau-Zener transitions, and the prepared pho-ton state as well as the measured quantum dot in an hybrid quantum dots-superconducting resonator system.The main content of this thesis includes:1. A brief introduction of some basic concepts of quantum computing, including the concepts of qubit, quantum logic gate, quantum simulation. Described the basic principles, experimental scheme and basic physics characteristics of semiconduc-tor quantum dots.2. From the design of semiconductor quantum dots, we studied the device simula-tion of the semiconductor quantum dots. Analysed the form of two-dimensional electron gas at the interface of GaAs/AlGaAs and the impact on energy band and two-dimensional electron gas due to the doping in the one dimensional model. On the basis, we simulate the three dimensional semiconductor gate controlled quan-tum dots with the method of Poisson-Schrodinger self-consistent solution. The charge stability honeycomb diagrams obtained were agreed with the measurement results of the experiments.3. Introduced the source, simulation and elimination of the decoherence in a two level system. We analysed the decoherence in the quantum dots using the nu-merical simulation, and found that the source of decoherence can be divided into intrinsic decoherence and extrinsic decoherence. Both of the two factors were contributed to the decoherence of quantum dots. Then we studied the impact on coherent dynamics of qubit due to the working parameters such as driven pulse shape. The result demonstrated the intrinsic qubit population leakage to unde-sired states can be minimized by choosing proper working parameters. This may improve the fidelity of quantum gates.4. Introduced Landau-Zener transition and Landau-Zener-Stuckelberg interference, and studied the Landau-Zener transition in a charge qubit formed by semicon-ductor double quantum dots. We achieved ultra-fast universal quantum logic gate with Landau-Zener-Stuckelberg interference, and extract the decoherence time in the Landau-Zener transition using the two dimensional fourier transform.5. From equilibrium phase transition, we introduced the Kibble-Zurek mechanism which describes the non-equilibrium phase transition. Take the one dimensional Ising spin chain for example, we introduced the analogy between the Kibble-Zurek mechanism and the Landau-Zener transition, and how to map the Kibble-Zurek mechanism to the Landau-Zener transition. There are two cases of quench: the slow quench and the fast quench, which performs different behavior. We sim-ulated Kibble-Zurek mechanism with Landau-Zener transitions experimentally, and found the relation between the topological defect density and the quench time in the two different quench cases, respectively.6. Introduced the basic physics model of the hybrid quantum dots-superconducting resonator system. Designed the experimental scheme of preparing photon state in the hybrid system by manipulating the quantum dots. And studied the mea-surement method to detected the quantum dots by resonator, which including the detection of the charge stability honeycomb diagram and the detection of the co-herent dynamics of qubits.The main innovations of this thesis are：1. Simulated the semiconductor gate controlled quantum dots with the method of Poisson-Schrodinger self-consistent solution, the results can improve the design of the quantum dots.2. Analysed the dynamics of quantum dots by numerical simulation. Found both of the intrinsic decoherence and extrinsic decoherence contributed to the deco-herence of quantum dots. Found it can improve the fidelity of quantum dots by optimizing the working parameters. These studies can enhance our understanding of decoherence in the quantum dots, making the high fidelity gate be possible. 3. Implemented the Landau-Zener transition in the quantum dots and analysed the Landau-Zener-Stuckelberg interference. On the basis, achieved ultra-fast univer-sal quantum logic gate in the quantum dots.4. Simulated the Kibble-Zurek mechanism with Landau-Zener transitions in exper-imental, obtained the scale law in the fast quench case. This was a proof-of-principle quantum simulation of the Kibble-Zurek mechanism in experimental.5. Studied the hybrid quantum dots-superconducting resonator system theoretically. Designed the experimental scheme of preparing photon state. Studied the mea-surement method to detect the quantum dots by resonator.