  We consider the simulation of interacting high-dimensional systems using
pairwise interacting qubits. The main tool in this context is the generation of
effective many-body interactions, and we examine a number of different
protocols for obtaining them. These methods include the usage of higher-order
processes (commutator method), unitary conjugation or graph state encoding, as
well as teleportation based approaches. We illustrate and compare these methods
in detail and analyze the time cost for simulation. In the second part of the
article, we investigate the influence of noise on the simulation process. We
concentrate on errors in the interaction Hamiltonians and consider two generic
noise models, (i) timing errors in pairwise interactions and (ii) noisy
pairwise interactions described by Master equations of Lindblad form. We
analyze and compare the effect of noise for the different simulation methods
and propose a way to significantly reduce the influence of noise by making use
of entanglement purification together with a teleportation based protocol.
