  We present a scheme to implement a universal set of quantum gates based on
achievable interactions, and the gates can be protected against decoherences
through dynamical-decoupling approach without encoding. By properly designing
system evolutions, the desired system interactions commute with the elements
forming dynamical decoupling pulses. Thus, the effect of decoherences can be
eliminated by repeatedly applying the pulses, without noticeably affecting the
system evolutions governed by the desired system interactions given small
enough time interval between pulses. Moreover, due to the commutation between
the elements forming the pulses and the desired system interactions, our scheme
is resistant to different types of decoherences, and so not limited to specific
decoherences. Our scheme also works well in the case that the desired system
interactions cannot be achieved ideally due to imperfect control of system
parameters, through the action of dynamical-decoupling pulses.
