由于半导体自旋电子学器件具有自旋相干时间长，数据处理快，功耗低等优点，引起了越来越多物理学家的注意。这种低功耗的固体自旋电子学器件非常有希望构造量子计算机的基础元件——逻辑门。因此，如何在半导体微结构中构造出一种可调相互作用，并使之符合量子逻辑门以及量子计算规则的要求，成为一个很有意义的热门问题。RKKY相互作用(Ruderman-Kittel-Kasuya-Yosida interaction)是一种局域自旋间以载流子来传递的间接相互作用，它不要求局域自旋之间有直接耦合，所以可能实现较远程的操纵。相对量子点等其他量子门的物理实现方案，基于RKKY相互作用的量子逻辑门具有自己的特点。本文从最基本的费米海中局域自旋间的RKKY相互作用出发，深入探讨了RKKY相互作用各个方面的特性。我们用Keldysh格林函数的方法分别计算了半导体低维电子气上只存在Rashba自旋轨道耦合时和同时存在Rashba与Dresselhaus两种自旋轨道耦合时的RKKY相互作用，并进而在后者的基础上构造出若干量子逻辑门。本文的结构如下：第一章我们概述了介观物理、自旋电子学和RKKY相互作用；第二章我们用量子力学二阶微扰理论推导出不考虑自旋轨道耦合时的半导体微结构中的RKKY相互作用，并分别计算了三种不同空间维度下的程函数，揭示了RKKY相互作用的振荡特征以及这种振荡对局域自旋间空间距离和半导体中电子数密度的依赖；第三章我们推导了用Keldysh格林函数表达的RKKY相互作用，并进而计算了一维和二维电子气上只考虑Rashba自旋轨道耦合时的RKKY相互作用；第四章我们利用上一章导出的公式，计算了一维电子气上同时考虑两种自旋轨道耦合时的RKKY相互作用，并利用系统的柱对称性把复杂的结果简化成一个简洁漂亮的形式。接着我们又对RKKY相互作用在各种不同参数下对可调变量的依赖作了细致的数值分析；第五章我们首先概述了量子门的一般性质，然后在第四章推导的RKKY相互作用形式的基础上通过两种不同的思路构造出通用的双量子比特门以及其他一些量子门。

Due to long spin coherence time, fast data processing and low powerconsumption in semiconductor spintronics device, physicists arepaying ever growing attentions to them. Low-power spintronicscomponents are very promising candidates for constructing elementaryparts of quantum computers——quantum logic gate. It is thereforefully legitimate to design quantum logic gates that based on antunable interaction in the semiconductor microstructures. RKKYinteraction is an indirect exchange interaction between local spinsmediated by the free carriers in materials and does not requiredirect coupling between local spins. Quantum gates based on RKKYinteraction do not prescribe close distance between local spins. Incontrast to other plans of physical realization for quantum gates,e.g. quantum dot, the quantum logic gates utilizing RKKY interactionexhibit unique interesting property. This thesis starts off with the RKKY interactions among local spins in fermi sea and thus furtherexplores the properties of RKKY interaction in different quantumstructures. We adopt the Keldysh Green's function approach tocalculate the range function of RKKY interactions for differentcases. One case is for the low-dimensional quantum structures in thepresence of Rashba spin-orbit coupling alone and the other caseincludes both Rashba and Dresselhaus spin-orbit couplings. We alsoproposed to construct quantum logic gates based on RKKY interactionin one-dimensional electron gas.This thesis is organized as follows: In Chapter One we brieflysummarize mesoscopic physics, spintronics and RKKY interaction; InChapter Two we use second-order perturbation theory to derive theRKKY interaction for different low-dimensional structures neglectingspin-orbit interaction. The range function of three-, two-, one-dimension electron gas are calculated respectively. The oscillatorycharacteristics of RKKY interaction and its dependence on thespatial distance between local spins as well as the electron numberdensity in the semiconductor are presented; In Chapter Three wederive the explicit expression of RKKY interaction utilizing theGreen's function of Keldysh formalism, for one dimensional electrongas as well as two dimensional electron gas in the presence ofRashba spin-orbit coupling alone; In Chapter Four we make uses ofthe formulas derived from the previous chapter to calculate RKKYinteraction for one dimensional electron gas, including both Rashbaspin-orbit interaction and Dresselhaus spin-orbit interaction.Considering cylindrical symmetry the results can be reduced to arather simple and beautiful expression. We also give detailed numerical results about the dependence of RKKYinteraction on different parameters; In Chapter Five we firstsummarize general properties of quantum gates and then use the RKKYinteraction formula derived in Chapter Four to construct universalbilateral qubit and quantum logic gates.