Robust quantum control by smooth quasi-square pulses

Robust time-optimal control is known to feature constant (square) pulses. We analyze fast adiabatic dynamics that preserve robustness by using alternative smooth quasi-square pulses, typically represented by hyper-Gaussian pulses. We here consider the two protocols, robust inverse optimization and time-contracted adiabatic passage, allowing the design of the same pulse shape in both cases. The dynamics and their performance are compared. The superiority of the former protocol is shown.