Topological quantum codes on surfaces with lattice defects

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The order of a system is dened by the way its constituents are organised with respect to each other. Such order characterises different phases of matter, with the quantum phase of a system referring to its ground state, ie. its lowest energy conguration. This project will conduct investigations in such two-dimensional systems, with added characteristics, namely emerging particles which can pick up any phases (statistics) under their mutual and self-exchange, hence their name. These are topological phases of matter, and were the subject of the 2016 Nobel Prize to Thouless, Kosterlitz, and Haldane. Moving a collection of anyons while intersecting their paths in specific ways is referred to as braiding their worldlines, and gives rise to logic gates that can be used for computation and other forms of information processing. Direct applications of studies of these systems would be topological quantum memories allowing to \free up more hardware", topological quantum computers for diverse calculations and simulations, and the construction of error-correcting schemes rendering quantum computation robust to local perturbations which are bound to arise in experimental quantum set-ups.This PhD project will study exotic properties of topological phases of matter, in lattice systems with interesting engineered defects, and will be conducted with the general aim of contributing to quantum informational and computational schemes towards reliable fault-tolerant quantum computation, while also providing a ground for exploratory work on fundamental condensed matter and topological quantum physics using quantum information tools.