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

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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.