  We present a method to accelerate the dynamical evolution of multiqubit open
system by employing dynamical decoupling pulses (DDPs) when the qubits are
initially in W-type states. It is found that this speed-up evolution can be
achieved in both of the weak-coupling regime and the strong-coupling regime.
The physical mechanism behind the acceleration evolution is explained as the
result of the joint action of the non-Markovianity of reservoirs and the
excited-state population of qubits. It is shown that both of the
non-Markovianity and the excited-state population can be controlled by DDPs to
realize the quantum speed-up.
