The central aim is to propose a topological quantum computation model that can be implemented with current or near future technology. To achieve this we will integrate recent advances in algebraic representation theory and integrable systems with theoretical advances in the understanding of topological phases of matter, and with the capabilities of current experiments. We aim to propose realisations of topological models in new physical systems such as topological insulators, and so to harness their properties for quantum computation applications.
Strategically, then, the objective is to create a timely new interdisciplinary area at Leeds, melding the relevant strengths in Mathematics and Physics.
The overarching scientific objectives of the project are summarized as follows.
- Study topological insulators and the non-Abelian anyonic excitations at their boundary by constructing analytically tractable examples.
- Place the algebraic and wider theoretical formalism for anyonic systems on a sufficiently general footing that serves to frame the full range of candidate solutions and identify appropriate topological models corresponding to particular representations of the algebra of these anyonic systems, that are complex enough to support universal quantum computation, but simple enough to be physically realizable.
- Explore radical new schemes for topological error protection via, for example, the lattice realisation of topological structures arising in quantum geometry.
- Build efficient, robust topological quantum memories by employing Anderson localisation.
- Identify appropriate topological models corresponding to particular representations of the general algebra in 2., that are complex enough to support universal quantum computation, but simple enough to be physically realizable.
- Manipulate encoded quantum information with simple, achievable controls, e.g. lattice site measurements or quantum gates, in a way that preserves topological protection.
- Propose a scalable system based on topological insulators that perform topological quantum computation.