Optimal control inspired algorithm for real-space optimization with application to Majorana fermion experiments

Inspired by the success of optimal control theory algorithms in the design of new, fast and accurate gates for quantum information processing, we import the mindset of these time-domain optimization strategies to static real-space functions in solid-state systems. Combining ideas from the GRAPE (Gradient Ascent Pulse Engineering) algorithm and transport calculations, we devise a new gradient-based algorithm for the optimization of transport-related quantities through the real-space variation of experimentally controllable parameters. This technique can be useful for the design of experiments in mesoscopic solid-state systems. As an example, we apply our algorithm to the optimization of the topological visibility of Majorana fermions in superconducting nanowires without spin-orbit coupling in a non-uniform magnetic field.