An intriguing way to reinvent the error-robustness of classical digital computing is to work with topological characteristics of the ‘computer components’ — that is, characteristics that are invariant under small local distortions of the system (which are typically the main kind of error inducing ‘noise’ present).
Our research is concerned with the investigation of topological systems that can support quantum information tasks, such as quantum memory, quantum computation and quantum cryptography. The goal is to propose small-scale topological models, amenable to laboratory simulations, which would then test their feasibility as models for quantum computation. The physics behind the models may be described in terms of ‘anyon’ particles, which can be experimentally realized in topological insulators or the fractional quantum Hall effect. Anyons can encode and manipulate quantum information error-robustly.
Our objective is to develop the theoretical underpinnings of this technology by means of the relation to certain algebraic structures and corresponding problems in low-dimensional topology and representation theory. In particular, while guided firmly by the requirements of physical realisability, our research endeavors to deepen the understanding of numerically and analytically solvable models arising from theoretical constructs such as generalized Temperley-Lieb diagram categories, as well as novel models of quantum geometry developed through the theory of exactly integrable quantum systems.