半导体量子点系统的理论与模拟
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摘要
量子计算是当前物理学领域的一个重要课题,半导体量子点是量子计算的一个主要的物理实现方案。本论文针对于半导体量子点的操作与测量等关键性问题,进行了理论研究和模拟计算,主要研究了两个方面的问题：一是如何设计更好的量子点,包括对半导体量子点的仿真,以及对量子点中退相干的分析；二是用量子点做什么,包括用Landau-Zener-Stuckelberg干涉实现超快普适的量子逻辑门操作,用Landau-Zener跃迁模拟非平衡相变的Kibble-Zurek机制,用量子点-超导传输线腔耦合系统制备超导传输线腔里的光子态和测量量子点。
本论文的主要内容有：
1.简要介绍量子计算的一些基本概念。对量子计算所涉及到的量子比特,量子逻辑门操作,量子模拟等基础概念进行了说明。阐述了半导体门控型量子点量子计算体系的原理基础,实验方案以及一些基本物理特征。
2.从半导体门控量子点的设计出发,研究了对半导体门控量子点的仿真。分析了量子点的一维模型中如何在GaAs/AlGaAs分界面处形成二维电子气,以及掺杂对能带结构和二维电子气的影响。在此基础上,使用Poisson-Schrodinger自洽求解的方法来对三维的半导体门控量子点进行仿真,仿真得出的量子点电荷稳态蜂窝图与实验结果吻合。
3.介绍了二能级体系上的退相干的产生来源、模拟方法与一些基本消除手段。使用数值模拟的方式,分析了量子点中存在的退相干,将退相干的来源分为固有退相干和外在退相干,这两种因素都对量子点的退相干有贡献。在考虑量子点到非设计态的耗散的情况下,研究了工作参数(如操作脉冲的波形)对演化过程的影响,结果表明通过优化工作参数,可以制作出更高保真度的量子门操作。
4.介绍了Landau-Zener跃迁和Landau-Zener-Stiickelberg干涉的基本概念。研究了半导体双量子点的电荷量子比特中的Landau-Zener跃迁过程。利用两通道Landau-Zener-Stiickelberg干涉实现了半导体量子点上的超快普适的量子逻辑门操作。用二维傅里叶频谱的方法提取出了量子点的Landau-Zener跃迁实验的退相干时间。
5.从平衡的Landau二级相变出发,介绍了非平衡相变的Kibble-Zurek机制。以一维Ising自旋链为例,介绍了Kibble-Zurek机制与Landau-Zener跃迁之间的对应关系,并将其分为快速淬火和慢速淬火两种不同的情况。在实验上利用半导体电荷量子比特的Landau-Zener跃迁过程模拟了Kibble-Zurek机制,得到了两种不同淬火情况下的拓扑缺陷密度与淬火时间之间的关系。
6.介绍了量子点-超导传输线腔耦合系统的基本物理模型。设计了用量子点来制备超导传输线腔中光子态的实验方案。研究了用超导传输线腔探测量子点的测量技术,包括对电荷稳态蜂窝图的探测和对量子点演化过程的探测。本论文的主要创新点有：
1.利用Poisson-Schrodinger自洽求解的方法对半导体门控量子点进行了仿真。仿真的结果能促进量子点结构的设计。
2.使用数值模拟的方式分析量子点的演化过程,发现固有退相干和外在退相干都对量子点的退相干有贡献。发现优化工作参数能提高量子点演化过程的保真度。这些研究能增强对量子点中的退相干的了解,设计出更高保真度的量子门操作。
3.实现了量子点上的Landau-Zener跃迁,分析了量子点上的Landau-Zener-Stuckelberg干涉过程。并以此为基础,实现了量子点上的普适超快的量子点量子逻辑门操作。
4.利用实验上实现的量子点上的Landau-Zener跃迁,模拟了非平衡相变的Kibble-Zurek机制,并得出了快速淬火情况下的标度律关系。这是对半导体量子点实现量子模拟的一个原理性验证。
5.理论上研究了量子点-超导传输线腔耦合系统。设计了用量子点来制备超导传输线腔中光子态的实验方案。研究了用超导传输线腔探测量子点的测量技术,包括对电荷稳态蜂窝图的探测和对量子点演化过程的探测。
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.
本论文的主要内容有：
1.简要介绍量子计算的一些基本概念。对量子计算所涉及到的量子比特,量子逻辑门操作,量子模拟等基础概念进行了说明。阐述了半导体门控型量子点量子计算体系的原理基础,实验方案以及一些基本物理特征。
2.从半导体门控量子点的设计出发,研究了对半导体门控量子点的仿真。分析了量子点的一维模型中如何在GaAs/AlGaAs分界面处形成二维电子气,以及掺杂对能带结构和二维电子气的影响。在此基础上,使用Poisson-Schrodinger自洽求解的方法来对三维的半导体门控量子点进行仿真,仿真得出的量子点电荷稳态蜂窝图与实验结果吻合。
3.介绍了二能级体系上的退相干的产生来源、模拟方法与一些基本消除手段。使用数值模拟的方式,分析了量子点中存在的退相干,将退相干的来源分为固有退相干和外在退相干,这两种因素都对量子点的退相干有贡献。在考虑量子点到非设计态的耗散的情况下,研究了工作参数(如操作脉冲的波形)对演化过程的影响,结果表明通过优化工作参数,可以制作出更高保真度的量子门操作。
4.介绍了Landau-Zener跃迁和Landau-Zener-Stiickelberg干涉的基本概念。研究了半导体双量子点的电荷量子比特中的Landau-Zener跃迁过程。利用两通道Landau-Zener-Stiickelberg干涉实现了半导体量子点上的超快普适的量子逻辑门操作。用二维傅里叶频谱的方法提取出了量子点的Landau-Zener跃迁实验的退相干时间。
5.从平衡的Landau二级相变出发,介绍了非平衡相变的Kibble-Zurek机制。以一维Ising自旋链为例,介绍了Kibble-Zurek机制与Landau-Zener跃迁之间的对应关系,并将其分为快速淬火和慢速淬火两种不同的情况。在实验上利用半导体电荷量子比特的Landau-Zener跃迁过程模拟了Kibble-Zurek机制,得到了两种不同淬火情况下的拓扑缺陷密度与淬火时间之间的关系。
6.介绍了量子点-超导传输线腔耦合系统的基本物理模型。设计了用量子点来制备超导传输线腔中光子态的实验方案。研究了用超导传输线腔探测量子点的测量技术,包括对电荷稳态蜂窝图的探测和对量子点演化过程的探测。本论文的主要创新点有：
1.利用Poisson-Schrodinger自洽求解的方法对半导体门控量子点进行了仿真。仿真的结果能促进量子点结构的设计。
2.使用数值模拟的方式分析量子点的演化过程,发现固有退相干和外在退相干都对量子点的退相干有贡献。发现优化工作参数能提高量子点演化过程的保真度。这些研究能增强对量子点中的退相干的了解,设计出更高保真度的量子门操作。
3.实现了量子点上的Landau-Zener跃迁,分析了量子点上的Landau-Zener-Stuckelberg干涉过程。并以此为基础,实现了量子点上的普适超快的量子点量子逻辑门操作。
4.利用实验上实现的量子点上的Landau-Zener跃迁,模拟了非平衡相变的Kibble-Zurek机制,并得出了快速淬火情况下的标度律关系。这是对半导体量子点实现量子模拟的一个原理性验证。
5.理论上研究了量子点-超导传输线腔耦合系统。设计了用量子点来制备超导传输线腔中光子态的实验方案。研究了用超导传输线腔探测量子点的测量技术,包括对电荷稳态蜂窝图的探测和对量子点演化过程的探测。
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.
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