  In this work, we study quantum evolution of an open moving-qubit modulated by
a classical driving field. We obtain the density operator of qubit at zero
temperature and analyze its quantum evolution dynamics by using quantum speed
limit time (QSLT) and a non-Markovianity measure introduced recently. The
results show that both the non-Markovian environment and the classical driving
can speed up the evolution process, this quantum speedup process is induced by
the non-Markovianity and the critical points only depend on the qubit velocity.
Moreover, the qubit motion will delay the evolution process, but this negative
effect of the qubit velocity on the quantum speedup can be suppressed by the
classical driving. Finally, we give the corresponding physical explanation by
using the decoherence rates.
