Modeling ABS Energy & Density Character for Topological Josephson Junctions Augmented by Nanowire Architecture

The worldwide quantum computing (QC) enterprise has been met with success over the past two decades. The field has produced sophisticated algorithms to address far reaching problems, and the hardware has made large strides towards robust systems with qubit coherence times increasing yearly for all types. However, it has become apparent that the noisy quantum environment is a larger threat than many may realize with some predicting an inflection point within a decade. Whether or not this is true obviously remains to be seen, but we should ask, will we be able to escape the NISQ era of QC or will the early visions of quantum supremacy be severely restricted by an impenetrable hardware limitation? In this talk, we address a small part of the problem by adopting a well-known strategy of incorporating topological materials into the qubit design, handling decoherence from a hardware level. We will first provide an overview of the role of topological and superconducting materials in QC, followed by our work where we model several Josephson junctions that are modified by the presence of topological superconducting nanowires in between their host superconductors. Of key interest to the theoretical modelling of qubit dynamics are the energy-phase relationship and spatial character of the Andreev bound states (ABS) therein. These quantities are calculated for a catalogue of simplistic topological Josephson junctions to provide insight into their design and to inform the engineering of more complicated systems.