Universal simulation of Markovian quantum dynamics

In search for a way to simulate the dynamics of open quantum systems using a simple set of primitives, a framework was set up to study the notion of universality for Markovian quantum dynamics. It was shown how the generators of Markovian semigroups transform under the composition procedures of linear combination unitary conjugation. For the case of a single qubit, it was illustrated that one primitive unital operation suffices to simulate all other unital operations. A sufficient and necessary single-parameter universal set for general qubit Markovian quantum dynamics was derived.