  Although the conditions for performing arbitrary unitary operations to
simulate the dynamics of a closed quantum system are well understood, the same
is not true of the more general class of quantum operations (also known as
superoperators) corresponding to the dynamics of open quantum systems. We
propose a framework for the generation of Markovian quantum dynamics and study
the resources needed for universality. For the case of a single qubit, we show
that a single nonunitary process is necessary and sufficient to generate all
unital Markovian quantum dynamics, whereas a set of processes parametrized by
one continuous parameter is needed in general. We also obtain preliminary
results for the unital case in higher dimensions.
