Quantum computers are thought to be the future of computation, using the properties of quantum mechanics to solve problems intractable to classical computers. Quantum computing leverages non-classical properties, such as entanglement, to achieve an exponential improvement in computational power. A quantum computer would enable us to address many real-world problems, such as how to synthesize fertilizers more efficiently; how to combat global warming; or to simulate protein folding in biological systems. Although much work has been done to describe the use and implementation of entanglement generation theoretically, it is still a challenge to develop such protocols experimentally. The bulk of this work is focused on creating Graphics Processing Unit (GPU)-accelerated computer simulations of quantum systems with advanced numerical and analytical techniques. Simulations can guide experiments attempting to create building blocks of quantum computers - qubits and their control devices. However, simulation of more realistic device setups in two dimensional systems has been facing problems owing to the space and time domain scaling associated with the solutions of the many-particle time dependent Schrodinger equation (TDSE). Nevertheless, recent advances in computer hardware performance has made previously intractable two-particle problems readily solvable. I have developed custom GPU-accelerated software based on a staggered-leapfrog algorithm that opens up new possibilities of simulating two-dimensional two-particle systems accurately.

I focus on three research projects. Firstly, optimally defining a charge-based solid state qubit, and controlling it in a simple and experimentally achievable way, while accounting for imperfections of the waveform generators. I simulate the physical qubit on a fine-grained lattice, and propose an innovative control scheme that accounts for finite rise/fall time of the experimental apparatus, while being relatively fast and resulting in very high operation fidelity. An optimal pulsing scheme with rise time-dependent parameters is found, and shown to be able to achieve an arbitrary qubit rotation. Since the proposed pulse sequence reduces to sine waves to minimize total pulse duration, it is straightforward to implement experimentally, and easily generalisable to different systems. I also show how the fidelity remains sufficiently high independently of the initial qubit state. The proposed sequence can even reduce errors caused by charge noise under certain conditions. Readout techniques are discussed as well, and found to not present significant issues.

Secondly, I aid the effort to create a Surface Acoustic Wave quantum computer prototype by describing how to produce an universal quantum gate set with a Root-of-SWAP operation used as a physical two-qubit gate. Using realistic parameters, it is shown how this operation can be performed with high fidelity. Previous work has been done to simulate a proposed Root-of-SWAP method in one dimension - this work focuses on extending this to two dimensions.

We find that the method of generating Root-of-SWAP mentioned above breaks down in two dimensions- unwanted excitations are introduced in the extra dimension, causing a phase difference to appear, and thus ruining coherence of the state.

I propose to implement the Root-of-SWAP operation via a tunneling interaction across the effective double dot instead. This was previously considered, however was thought to be unstable against variations in tunnel barrier height, which has exponential impact on the speed of the quantum operation. Using newly available computing power, we were able to run detailed two dimensional simulations investigating this method and its robustness against variations in the double dot potential. We find that the method produces high fidelity Root-of-SWAP states, and is robust against small variations in the tunnel barrier. Additionally, we find a relation between the tunnel barrier height and spin measurement probability, providing a way for experimentalists to estimate an actual device barrier indirectly.

Finally, I theoretically model and simulate transport through a single electron transistor (SET) device. It is shown that a single donor structure can reliably be engineered from doped quantum dots by taking advantage of the tunability of the electron tunneling rates as well as the interplay, at low temperatures, between disorder conferred by randomness in dopant distribution and electron-electron interaction originating from the high doping concentration. It is possible to electrostatically isolate a single donor from the large ensemble of dopants. I investigate how such a complex system is expected to conduct, and verify a hypothesis that two donors take part in the transport by numerically reproducing the experimental measurements. Finally, it is shown that this device can be used as a single atom detector of the charge occupancy of a nearby capacitively coupled double quantum dot. While this final part does not make use of the GPU-accelerated software, it is still closely related to the rest of this work, and the theme of modeling realistic quantum devices.