  Accurate control of quantum evolution is an essential requirement for quantum
state engineering, laser chemistry, quantum information and quantum computing.
Conditions of controllability for systems with a finite number of energy levels
have been extensively studied. By contrast, results for controllability in
infinite dimensions have been mostly negative, stating that full control cannot
be achieved with a finite dimensional control Lie algebra. Here we show that by
adding a discrete operation to a Lie algebra it is possible to obtain full
control in infinite dimensions with a small number of control operators.
