Quantum control robust with coupling with an external environment

We study coherent quantum control strategy which is robust with respect to coupling with an external environment. We model this interaction by appending an additional subsystem to the initial system and we choose the strength of the coupling to be proportional to the magnitude of the control pulses. Therefore, to minimize the interaction we impose $L_1$ norm restrictions on the control pulses. In order to efficiently solve this optimization problem we employ the BFGS algorithm. We use three different functions as the derivative of the $L1$ norm of control pulses: the signum function, a fractional derivative $\frac{\dd^\alpha |x|}{\dd x^\alpha}$, where $0<\alpha<1$, and the Fermi-Dirac distribution. We show that our method allows to efficiently obtain the control pulses which neglect the coupling with an external environment.