李雅普诺夫控制方法在半导体量子点状态转移中的应用

发布时间：2018-04-10 22:11

本文选题：半导体量子点 + 量子位　；参考：《中国科学技术大学》2015年硕士论文

【摘要】：量子计算是近年来是国际上最热门的研究前沿课题之一,实现量子计算的最大挑战是多量子位的操纵。在操纵量子位的物理系统中,半导体量子点以其成熟的半导体制作工艺和良好的可扩展性赢得了人们的广泛关注和研究。在半导体量子点的量子位状态转移研究中,物理学家已经能够利用LZS (Landau-Zener-Stiicklberge)干涉原理设计出实现量子位状态转移的控制外场。在系统控制理论中,量子李雅普诺夫控制方法经过多年的发展,已在量子系统的状态制备与操纵方面取得了显著的成果,如叠加态的制备、状态轨迹跟踪、基于李雅普诺夫方法的最优控制和开关控制的状态转移等。本论文应用李雅普诺夫控制方法,为半导体双量子点系统设计出满足实际物理系统和脉冲发生器要求的控制律,实现双量子点系统量子位的高性能状态转移,并通过系统仿真实验验证所设计控制律的有效性和实用性。主要研究内容分两部分： 1.基于李雅普诺夫控制方法的二能级双量子点量子位超快操纵。首先研究半导体双量子点物理系统,学习系统哈密顿量模型,利用开放马尔科夫系统模型研究系统状态演化规律。然后基于李雅普诺夫稳定性定理,针对双量子点系统设计出保证系统状态进行快速转移的控制律；利用Matlab进行系统仿真实验验证所设计控制律的有效性。最后将基于李雅普诺夫控制方法的量子位状态转移性能与基于LZS干涉原理的性能进行对比分析,通过对比实验结果得出结论：在李雅普诺夫控制场作用下系统状态从|R转移到|L的性能较LZS干涉原理的性能相比具有更高状态转移概率和更短状态转移时间；李雅普诺夫控制场能够对状态转移过程中消相干引起的耗散进行有效地补偿,使系统对消相干有较强的鲁棒性,系统状态转移能获得较高的保真度；量子李雅普诺夫控制方法设计的控制场比LZS干涉原理设计的控制场有明显的优越性。 2.可实现的李雅普诺夫操纵方法的设计。最初利用李雅普诺夫控制方法设计出的控制律从理论上证实了此方法能够实现半导体量子点系统的状态转移,然而由于实际物理系统和激光脉冲发生器的性能限制,需要对此方法设计的控制律进行改进才能应用于实际实验。首先再次考察半导体双量子点物理系统的限制条件和激光脉冲发生器的性能参数,规划所设计的控制律应具有的具体形式。然后基于李雅普诺夫稳定性定理对所设计的控制律进行改进,得到便于在实际实验中实现的控制律具体形式。在Matlab中验证在改进控制场作用下系统的状态转移性能,并与基于LZS干涉原理的性能进行对比分析。系统仿真实验研究了不同控制参数条件下系统的状态转移性能和控制律的形式,实验结果表明：在满足Agilent81134A脉冲发生器最小上升时间～75ps和Tektronix AWG70000A脉冲发生器最小上升时间～20ps的前提下,所设计的控制场能保证系统的状态转移概率分别达到在～85%和～96%以上；系统的保真度能提高到94%以上；与基于LZS干涉原理实现的状态转移的性能相比,本论文基于李雅普诺夫稳定性定理设计出的改进控制场的状态转移性能有明显的优越性。
[Abstract]:Quantum computation is one of the most popular research topic internationally in recent years, the biggest challenge to realize quantum computation is the manipulation of multi qubit qubit system. In the physical manipulation of semiconductor quantum dots in mature semiconductor fabrication and good scalability of won wide attention and research in semiconductor quantum people. The qubit state transfer study, physicists have been able to use LZS (Landau-Zener-Stiicklberge) is designed to realize the control principle of interference field qubit state transition. The system control theory, quantum Lyapunov control method after years of development, has made remarkable achievements in the state of preparation and manipulation of quantum systems, such as the superposition state preparation, trajectory tracking, optimal control and switch control Lyapunov method based on state transition.
The application of Lyapunov control method for semiconductor double quantum dot system designed to meet the actual physical system and pulse generator control law requirements of the state to achieve high performance double quantum dot qubit transfer, and through simulation experiments verify the effectiveness and practicability of the design of control laws. The main research content is divided into two parts:
1. Lyapunov based control method for two level double quantum dot qubit ultrafast manipulation. First study the double quantum dot semiconductor physics system, learning system Hamiltonian model, using Markov system open research system model evolution. Then based on Lyapunov stability theorem, the double quantum dot system is designed to ensure the rapid transfer of control law the state of the system; the use of Matlab system simulation experiments verify the effectiveness of the control law. The transfer properties of the Lyapunov control method based on the qubit state and performance of LZS interference based on the principle of comparative analysis, by comparing the experimental results concluded that: in the Lyapunov control system state transition field from |R to |L the performance is better than the performance of the LZS interference principle compared with higher transfer state probability and state transition time shorter Ivanov; control Lyapunov field can effectively compensate for the dissipation caused by coherent state transition in the process of elimination, the system of decoherence has a strong robustness, the system state transfer can obtain high fidelity; quantum control design method of control Lyapunov field ratio control principle of LZS interferometer design field superiority the obvious.
2. design can realize the Lyapunov control method. Using the initial control Lyapunov control method designed theoretically proved this method can realize the semiconductor quantum dot system state transition, but due to the actual physical system and the laser pulse generator can limit, need to control law design method was improved in this regard can be used in the actual experiment. First, we investigate semiconductor double quantum dot system physical constraints and laser pulse generator performance parameters, the concrete form of control law design planning should have. Then the Lyapunov stability theorem to improve the control law based on the design, we have obtained the control law of the realization in the actual experiment the in Matlab testing to improve the control field under the action of the state transition of the system performance, and the performance of LZS based on the interference principle Comparison and analysis. System simulation experiments on different control parameters of the system under the condition of the state transfer and control law, the experimental results show that the Agilent81134A meet the minimum rise time of pulse generator and Tektronix pulse generator AWG70000A ~ 75ps ~ 20ps minimum rise time, the design of the control system can guarantee the state transfer the probability reached above 85% and in ~ ~ 96%; the system fidelity can increase to more than 94%; compared with the performance of the LZS interference principle realization based on state transition, the transfer has obvious advantages to improve the performance of control Li Yapu Lyapunov stability theorem to design field based on the state.

【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O471.1

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