Theoretical and computational study of spin and charge qubits trapped in single and double quantum dots formed by Surface Acoustic Waves (SAWs)

量子比特或量子比特是量子计算机的基本组成部分。目前，实现量子计算的两个主要障碍是错误和缺乏系统可伸缩性。因此，研究量子比特的物理实现以及如何对其进行逻辑运算是至关重要的。这是一个理论和计算项目，重点研究由声表面波(SAW)形成的单量子点和双量子点中的电荷和自旋量子比特。这个平台是一个有吸引力的量子计算实现，因为被SAW捕获的电子很容易纠缠，但由于限制而不会分散。它也可以使用现有的半导体制造工艺来实现。最初的工作是基于点的相干运动状态对电荷量子比特进行的。利用有限差分方法和有限元方法建立了精确的动力学模型和测量模型。开发了模拟量子动力学的软件，并在为该项目构建的两个定制内部图形处理单元(GPU)服务器上运行。该软件能够有效地求出系统的基态和激发态，并能在任意含时势下模拟系统的时间动力学。随着GPU处理能力的提高和软件的优化，我们能够在合理的时间内模拟数千个空间站点上的两粒子二维系统。研究了单电荷量子比特动力学，找到了任意量子比特旋转的最佳量子比特定义和方案，并通过模拟验证了这两种操作。对半导体器件中SAW携带的电子自旋量子比特的两种量子比特纠缠操作进行了研究，并对两种方法进行了比较。结果发现，基于交换相互作用的操作在实验上是可行的，而基于绝热碰撞的操作引入了显著的退相干，从而导致误差，因此在现实系统中是不可行的。接下来，电子自旋将以更明确和更一般的方式计入模型中，并将研究轨道和自旋纠缠之间的复杂相互作用。该软件还将扩展到模拟更一般的具有自旋的真实少粒子量子系统。通过应用密度矩阵形式，将包括完全退相干机制，这将使更深入地研究量子计算机中的错误是如何产生的，以及如何减轻这些错误。为该项目开发的软件和方法将对理论工作和实验者都有用，允许在特定设备中对量子动力学进行建模。

Qubits, or quantum bits, are the basic building blocks of a quantum computer. Currently, two major roadblocks for practical quantum computation are errors and lack of system scalability. It is therefore critical to study physical implementations of qubits, and how to carry out logical operations on them.This is a theoretical and computational project focused on studies of charge and spin qubits trapped in single and double quantum dots formed by Surface Acoustic Waves (SAWs). This platform is an attractive quantum computing implementation, as electrons trapped by SAWs are easy to entangle, but do not disperse due to confinement. It is also realisable using existing semiconductor manufacturing processes.The initial work was done on charge qubits based on coherent state of motion of the dots. An accurate model of dynamics and measurement was built, using finite difference and finite element methods. Software to simulate the quantum dynamics was developed, and is run on two custom in-house Graphics Processing Unit (GPU) servers that have been built for the project. The software is able to find the ground and excited states of the system efficiently, and to simulate the time dynamics of the system in an arbitrary time-dependent potential. With recent increases in GPU processing power and software optimisation, we are able to simulate two-particle two-dimensional systems on thousands of spatial sites in a reasonable time.Single charge qubit dynamics was investigated, and optimal qubit definition and scheme for arbitrary qubit rotation was found, and confirmed using simulations.Two qubit entangling operations were investigated for electron-spin qubits carried by SAWs in a semiconductor device, with two methods compared. It was found that the operation based on exchange interaction is experimentally feasible, while one based on adiabatic collision introduces significant decoherence leading to errors and is thus not viable in a realistic system. Next, electron spin will be included into the model in a more explicit and general way, and complex interplay between orbital and spin entanglement will be investigated. The software will also be extended to simulate more general realistic few-particle quantum systems with spin. Full decoherence mechanics will be included by applying the density matrix formalism, which will enable a more in-depth study of how errors arise in quantum computers, and how they can be mitigated. The software and methods developed for this project will be useful both for theoretical work and for experimentalists, allowing for modelling of quantum dynamics in a specific device.