Second order gradient ascent pulse engineering

[Display omitted] ► A fast optimal control procedure for NMR and ESR shaped pulse generation is presented. ► Exact propagator gradients with the BFGS Hessian are used to accelerate convergence. ► Detailed analysis of the numerical accuracy and performance is presented. We report some improvements to the gradient ascent pulse engineering (GRAPE) algorithm for optimal control of spin ensembles and other quantum systems. These include more accurate gradients, convergence acceleration using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton algorithm as well as faster control derivative calculation algorithms. In all test systems, the wall clock time and the convergence rates show a considerable improvement over the approximate gradient ascent.