The landscape of a quantum control problem for the generation of quantum gates of the phase shift type

Traps are points of local, but not global, extremum of the target quantum functional. Proof of the absence or presence of traps is important when investigating the landscape of a quantum control problem. Using analytical and numerical methods, we show that the problem of ultrafast generation of one-qubit phase-shift gates is free of traps. The report is based on joint work with O. V. Morzhin and A. N. Pechen.