Universal simulation of Markovian open quantum systems

We consider the problem of constructing a "universal set" of Markovian processes, such that any Markovian open quantum system, described by a one-parameter semigroup of quantum channels, can be simulated through sequential simulations of processes from the universal set. In particular, for quantum systems of dimension $d$, we explicitly construct a universal set of semigroup generators, parametrized by $d^2-3$ continuous parameters, and prove that a necessary and sufficient condition for the dynamical simulation of a $d$ dimensional Markovian quantum system is the ability to implement a) quantum channels from the semigroups generated by elements of the universal set of generators, and b) unitary operations on the system. Furthermore, we provide an explicit algorithm for simulating the dynamics of a Markovian open quantum system using this universal set of generators, and show that it is efficient, with respect to this universal set, when the number of distinct Lindblad operators (representing physical dissipation processes) scales polynomially with respect to the number of subsystems.