Qubits for topological quantum computation

Various topological quantum systems have been shown to be potentially viable as platforms
for quantum computation.
In this thesis we introduce two important topological models, the toric code model and the
Kitaev honeycomb model, and show that they have time-independent Hamiltonians that are
analytically solvable. We also look at the behaviour of anyons, generalisations of bosons and
fermions, that arise in these systems. We then investigate these systems with Hamiltonians
that have time-dependent control.
These systems are based on lattices of spin-1/2 particles which act as qubits. We are
interested in moving around anyons in these lattices, which requires investigation of timedependence
in the systems, where there is potential for errors to arise.
We therefore look at the dynamics of qubit systems, giving special attention to the Magnus
expansion, a method of approximating system dynamics with evolution that is always
unitary. We then use the Magnus expansion to study the effects of time-dependent control
and seek to examine how robust the systems continue to be, as well as under what conditions
the control preserves the important properties of these systems.

The main impact of the proposed Hub will be in training quantum engineers with a skillset to understand cutting-edge quantum research and a mindset toward developing this innovation, and the entrepreneurial skills to lead the market. This will grow the UK capacity in quantum technology. Through our programme, we nurture the best possible work force who can start new business in quantum technology. Our programme will provide multi-level skills training in quantum engineering in order to enhance the UK quantum technologies landscape at several stages. Through the training we will produce quantum engineers with training in innovation and entrepreneurship who will go into industry or quantum technology research positions with an understanding of innovation in quantum technology, and will bridge the gap between the quantum physicist and the classical engineer to accelerate quantum technology research and development. Our graduates will have to be entrepreneurial to start new business in quantum technology. By providing late-stage training for current researchers and engineers in industry, we will enhance the current landscape of the quantum technology industry. After the initial training composed of advanced course works, placements and short projects, our students will act as a catalyzer for collaboration among quantum technology researchers, which will accelerate the development of quantum technology in the UK. Our model actively encourages collaboration and partnerships between Imperial and national quantum tehcnology centres and we will continue to maintain the strong ties we have developed through the Centre for Doctoral Training in order to enhance our on-going training provisions. The Hub will also have an emphasis on industrial involvement. Through our new partnerships students will be exposed to a broad spectrum of non-academic research opportunities. An important impact of the Hub is in the research performed by the young researchers, PhD students and junior fellows. They will greatly enhance the research capacity in quantum technology. Imperial College has many leading engineers and quantum scientists. One of the important outcomes we expect through this Hub programme is for these academics to work together to translate the revolutionary ideas in quantum science to engineering and the market place. We also aim to influence industry and policy makers through our outreach programme in order to improve their awareness of this disruptive technology.