Geometric continuous dynamical decoupling with bounded controls

We develop a framework to implement the dynamical decoupling of open quantum systems using continuous pulse sequences. By exploiting the geometric perspective of the continuous dynamical decoupling, we show that the decoupling pulses can be intuitively designed in the basis of the structure function of the SU(n) corresponding to the control Hamiltonian. Several examples are given to illustrate the basic idea. We argue that in practice the efficiency of the decoupling is determined by the minimum attainable decoupling cycle time T-c instead of the order of the discrete decoupling group.