利用串联量子点晶体管测量固态量子比特

论文编号:WLX093  字数:11940,页数:30

摘     要
 
 本论文介绍了利用串联量子点测量固态量子比特的方法。首先简单介绍了当前量子输运和测量领域所用的基本方法，即Landauer-Büttiker散射矩阵理论以及量子主方程方法。通过建立测量模型的哈密顿量，得到了约化体系的量子主方程。这一方程决定了约化体系状态随时间的演化。约化体系状态有约化密度矩阵决定，其中包括对角元描述了量子态的概率，而非对角元则刻画了量子态的相干。本论文采用数值模拟的办法，演示了量子态（约化密度矩阵）随时间的演化，并着重分析了退相干机制。其中发现，退相干强度与测量仪器中的隧穿耦合紧密相关，即隧穿耦合增强（减弱）时，量子比特的退相干就相应地增加（减少）。最后，简要分析了能量重整化对量子测量的影响，并讨论了如何有效的描述量子测量过程中的测量时间和测量效率问题。

关键词：量子比特 量子测量 双量子点 约化动力学
Abstract
 This thesis is dedicated to the problem of quantum measurement of a solid-state qubit by a serially coupled double-dot detector. Two basic approaches in quantum transport and quantum measurement are first introduced, i.e. the Landauer-Büttiker scattering theory and the quantum master equation approach. By establishing the Hamiltonian of the measurement setup, the master equation for the reduced system is derived. This equation determines the time evolution of the state of the reduced system. The reduced state of the system is characterized by the reduced density matrix, which includes the diagonal elements describing the probabilities, and off-diagonal elements depicting the coherence of the quantum states. In this thesis, by employing the numerical simulation method, the time evolution of the quantum state is demonstrated, with the focus on the analysis of the dephasing mechanism. It is found that the dephasing rate is closely related to the tunnel coupling in the measurement device. As the tunnel coupling enhances (reduces), the corresponding decoherence would increase (decrease). Finally, the effect of energy renormalization on the measurement is briefly analyzed, and the measurement time and measurement efficiency are discussed.

Keywords：qubit; quantum measurement; double quantum dots; reduced dynamics

目  录
中文摘要……………………………………………………………………………………………  i
英文摘要……………………………………………………………………………………………  ii
目录………………………………………………………………………………………………… iii
第一章     绪论…………………………………………………………………………………… 1
 1.1  量子计算简介…………………………………………………………………………  1
 1.1.1 量子计算的发展………………………………………………………………  1
 1.1.2 量子计算的原理………………………………………………………………  1
 1.2  量子测量理论…………………………………………………………………………  2
       1.2.1 量子测量的观点………………………………………………………………  2
       1.2.2.定性概述………………………………………………………………………  2
       1.2.3 定量简介………………………………………………………………………  2
              1.2.3.1 可测量数据…………………………………………………………  2
              1.2.3.2 测量概率……………………………………………………………  3
 1.3  连续弱测量理论………………………………………………………………………  3
 1.4  量子点接触（QPC）测量背景介绍…………………………………………………   4
       1.4.1 QPC测量背景…………………………………………………………………   4
       1.4.2 QPC测量原理…………………………………………………………………   4
第二章     Landauer-Büttiker方法简介…………………………………………………………  6
 2.1   两端器件介绍………………………………………………………………………   6
 2.2   电流算符……………………………………………………………………………   7
 2.3   平均电流……………………………………………………………………………   8
第三章     量子主方程方法……………………………………………………………………   9
 3.1   体系描述……………………………………………………………………………   9
 3.2   二阶Born-Markov近似………………………………………………………………   9
 3.3   量子主方程…………………………………………………………………………  10
 3.4   与Landauer-Büttiker方法的比较………………………………………………  12
第四章     利用串联量子点测量量子比特……………………………………………………  13
 4.1  系统简介……………………………………………………………………………  13
 4.2  量子主方程…………………………………………………………………………  14
 4.3  约化动力学…………………………………………………………………………  15
  4.4  结果与讨论…………………………………………………………………………  21
第五章     展望…………………………………………………………………………………  22
 5.1  能量重整化效应……………………………………………………………………  22
 5.2  测量时间与测量效率………………………………………………………………  23
第六章     结论…………………………………………………………………………………  24
致谢………………………………………………………………………………………………   25
参考文献…………………………………………………………………………………………   26

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