  Dynamical decoupling represents an active approach towards the protection of
quantum memories and quantum gates. Because dynamical decoupling operations can
interfere with system's own time evolution, the protection of quantum gates is
more challenging than that of quantum states. In this work, we put forward a
simple but general approach towards the realization of higher-order protection
of quantum gates. The central idea of our approach is to engineer (hence regain
the control of) the quantum gate Hamiltonian in coordination with higher-order
dynamical decoupling sequences originally proposed for the protection of
quantum memories. In our computational examples presented for illustration, the
required engineering can be implemented by only quenching the phase of an
external driving field at particular times.
