One-Dimensional Topological States of Synthetic Quantum Matter

Topological states of matter are an influential concept of modern condensed matter physics with profound impact on our understanding of quantum phases. This dissertation is based on a collection of papers and addresses several questions on properties and applications of topological states in one-dimensional synthetic quantum systems. For example: - What is the fate of Majorana modes in systems with particle number conservation? - Can topologically protected edge modes be utilized for reliable transfer of quantum information? - How can one-dimensional topological quantum memories be implemented and corrected efficiently?