Explorando anyons em informações quânticas topológicas

Abstract

This dissertation presents a conceptual and mathematical introduction to the foundations of topological quantum computation, with emphasis on the emergence of non-Abelian anyons in two-dimensional systems. We start from the analysis of the configuration space of identical particles and build the quantum description through the language of Hilbert bundles, connections, and holonomy, making explicit the natural transition between topological concepts and their physical formulation. Within this framework, we show how Chern-Simons theory provides an effective model for the topological dynamics of anyonic systems, capturing the unitary transformations induced by fusion and braiding processes. From this structure, we discuss how these operations can be used to implement fault-tolerant quantum computation. The work has an essentially didactic character, aiming to elucidate the relationship between topology, geometry, and anyonic physics, highlighting the fundamental elements that support the proposal of topological computers.