  The success of quantum optimal control for both experimental and theoretical
objectives is connected to the topology of the corresponding control
landscapes, which are free from local traps if three conditions are met: (1)
the quantum system is controllable, (2) the Jacobian of the map from the
control field to the evolution operator is of full rank, and (3) there are no
constraints on the control field. This paper investigates how the violation of
assumption (3) affects gradient searches for globally optimal control fields.
The satisfaction of assumptions (1) and (2) ensures that the control landscape
lacks fundamental traps, but certain control constraints can still introduce
artificial traps. Proper management of these constraints is an issue of great
practical importance for numerical simulations as well as optimization in the
laboratory. Using optimal control simulations, we show that constraints on
quantities such as the number of control variables, the control duration, and
the field strength are potentially severe enough to prevent successful
optimization of the objective. For each such constraint, we show that exceeding
quantifiable limits can prevent gradient searches from reaching a globally
optimal solution. These results demonstrate that careful choice of relevant
control parameters helps to eliminate artificial traps and facilitate
successful optimization.
