Efficient real-space parameter optimization algorithm for Majorana nanowires

We present an efficient gradient-based method for the optimization of real-space parameter profiles in quasi-1D systems such as Majorana nanowires. Inspired by an analogy with the quantum optimal control algorithm GRAPE (Gradient Ascent Pulse Engineering), we can efficiently evaluate gradients of discretized real-space parameter profiles using analytical derivatives of recursive Green functions expressions. This new approach leads to a polynomial speedup over a simpler finite difference calculation. As an application, we optimize magnetic textures for the creation and stabilization of topological superconducting phases in nanowires without spin-orbit coupling. The optimization allows to go beyond intuitive and analytical results, leading to potentially new parameter regimes of experimental relevance in Majorana nanowires.