Long distance qubit-qubit coupling in silicon quantum dots

摘要：我研究了被困在半导体（如硅）和绝缘体界面上被称为量子点的小区域中的量子力学自旋之间的相互作用。即使电子的电场是球形的，电子也有方向，即自旋。自旋可以编码信息，这些信息可以在电场和磁场的帮助下进行控制。量子点中的电子自旋可以在所谓的稀释冰箱提供的寒冷环境中进行研究，这种冰箱可以将量子点及其周围环境冷却到非常接近绝对零度。需要这样的低温来区分这些微小粒子传输的微弱信号和不可避免的嘈杂环境引起的信号。为了充分处理包含在自旋中的信息，它们需要以一种定义良好的方式相互作用。我研究的相互作用可以看作是两个事实的相互作用。首先，两个电子由于具有相同特征的电荷而相互排斥。第二，两个具有完全相同能量和方向的电子不可能占据完全相同的物理空间。在两个相邻电子被捕获的系统中，它们会反复交换自旋方向。这种效应被称为交换相互作用。事实证明，在一个由三个或更多量子点电子组成的系统中，外层电子也可以通过自旋交换相互作用。我们的目标是应用这种效应来证明量子比特-量子比特之间的相互作用，与量子点尺寸相比，距离更长。特别是，我们的目标是研究由此产生的双量子比特门的可控性和质量。如果足够强大和可控，这种相互作用将是实现可扩展量子比特处理器的有益一步。

Abstract: I study the interaction between quantum mechanical spins controllably trapped in small regions known as quantum dots at the interfaces of a semiconductor, such as silicon, and and an insulator. Even though the electric field of an electron is spherical, electrons have orientation, the spin. Spins can encode information, which can be controlled with the help of electric and magnetic fields. Electron spins in quantum dots can be studied in cold environments provided by so-called dilution refrigerators, which cool them and their immediate environment down very close to absolute zero. Such cold temperatures are required to differentiate the faint signals transmitted by these tiny particles from the ones caused by inevitably noisy environment. To fully process the information contained in spins, they need to interact with one another in a well-defined manner. I study an interaction which can be seen as an interplay of two facts. First, two electrons repel each other due to both having a charge with the same signature. Second, two electrons with exactly the same energy and orientation cannot occupy exactly the same physical space. In systems where two nearby electrons are trapped, they repeatedly swap their spin orientations with one another. This effect is known as the exchange interaction. It turns out that the outer electrons in a system of three or more quantum dot electrons can also interact via spin exchange. We aim to apply this effect to demonstrate qubit-qubit interactions over distances that are long compared to quantum dot sizes. In particular, we aim to study the controllability and quality of the resulting two-qubit gates. If sufficiently strong and controllable, such and interaction would be a helpful step towards realising scalable qubit processors.