The realization of a quantum computer requires the development of a scaleable and reliable two-level system. This thesis presents the knowledge gained from experimenting with a series of low-dimensional hybrid superconductor/semiconductor quantum devices to investigate topological superconductivity. A topological superconductor is expected to host Majorana zero modes (MZMs) at its boundaries that are described by a non-local wavefunction obeying non-abelian exchange statistics. These attributes of MZMs enable the critical ‘faulttolerant’ quantum computation, whereby quantum information is stored in the fermionic parity of a non-local state. This method of encoding is predictedto protect quantum information from local noise sources, allowing for longer qubit lifetimes. This work extends beyond local tunneling spectroscopy signatures of MZMs on proximitized nanowires and focuses on investigating non-locality and Majorana parity that requires two-dimensional device geometries. My dissertation demonstrates that two-dimensional InAs-Al heterostructures are an encouraging material system for investigating topological superconductivity. This platform allows for conventional top-down fabrication, facilitating scalable device geometries necessary for pursuing topological qubit networks. A series of device geometries ranging in complexity were investigated to assess the feasibility of creating the first topological qubit using twodimensional heterostructures.The essential findings include the observation of conductance oscillations through a Majorana island interferometer with a flux period of h/e (h is Planck’s constant; e is the elementary charge). This indicates coherent transport of single electrons through the islands - a signature of Majorana non-locality. I demonstrate the progress that was made towards parityto-charge conversion for detecting the two parity states of a topological qubit. This includes the observation of transport signatures of zero-energy mode hybridization that are compatible with predictions of MZM hybridization. Finally, I introduce a fully two-dimensional platform based on a Josephson junction that enables a flux controlled topological phase transition. I report on transport signatures consistent with the observation of MZMs in a topological Josephson junction. The primary implication of this work is that two-dimensional heterostructures offer a promising platform for scalable topological quantum computation.