Optimally robust shortcuts to population inversion in two-level quantum   systems
  We examine the stability versus different types of perturbations of recently proposed shortcuts-to-adiabaticity to speed up the population inversion of a two-level quantum system. We find optimally robust processes using invariant based engineering of the Hamiltonian. Amplitude noise and systematic errors require different optimal protocols. 
A. Ruschhaupt, Xi Chen, D. Alonso and J. G. Muga
quant-ph