Robust transitionless quantum driving: Concatenated approach

We propose a concatenated approach for implementing transitionless quantum driving regardless of adiabatic conditions while being robustness with respect to all kinds of systematic errors induced by pulse duration, pulse amplitude, detunings, and Stark shift, etc. The current approach is particularly efficient for all time-dependent pulses with arbitrary shape, and only the phase differences between pulses is required to properly modulate. The simple physical implementation without the help of pulse shaping techniques or extra pulses makes this approach quite universal and provides a different avenue for robust quantum control by the time-dependent Hamiltonian.