Quantum computers have now reached capabilities where significant gate sequences can be executed. In some examples these gate sequences can even no longer be simulated classically. Nonetheless, implementing quantum error correction, which would allow for universal quantum computing, requires further heroic improvements. The current state is thus often termed “noisy intermediate scale quantum computing”. Together with some introduction to the subject, I’ll describe in this talk two examples how my group in Erlangen contributes to this line of research. One example is a scheme to realize a multi-qubit gate, the other is a strategy to reduce the number of gates needed for the simulation of quantum dynamics.