  We study the effect of an ancillary system on the quantum speed limit time in
different non-Markovian environments. Through employing an ancillary system
coupled with the quantum system of interest via hopping interaction and
investigating the cases that both the quantum system and ancillary system
interact with their independent/common environment, and the case that only the
system of interest interacts with the environment, we find that the quantum
speed limit time will become shorter with enhancing the interaction between the
system and environment and show periodic oscillation phenomena along with the
hopping interaction between the quantum system and ancillary system increasing.
The results indicate that the hopping interaction with the ancillary system and
the structure of environment determine the degree of which the evolution of the
quantum system can be accelerated.
