  Majorana zero modes (MZMs) realize a representation of non-abelian braid
groups that enable topological quantum computation, wherein the storage and
manipulation of information occur in decoherence-free degrees of freedom. This
paper is intended to build off existing texts in the topic [1, 2] to serve as
an introduction to MZMs at the undergraduate level, providing an overview of
many important concepts in condensed matter physics, such as the Bogoliubov-de
Gennes formalism and topological phases. We provide an overview of the
motivation behind finding MZMs and discuss how the nature of these modes can
provide an elegant solution to various challenges in quantum computing. We then
show how MZMs can appear in a toy model known as a Kitaev wire by solving its
spectrum, and conclude with a discussion on the conditions under which they
arise in a one-dimensional chain.
