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Which algorithms could you run on a given quantum device? I give an introduction into the concept of "reachable operations" in controlled quantum systems. In practice, quantum devices will be noisy, so it is important to characterise the reachable set of open quantum systems. This, however, brings many mathematical challenges, which I will briefly discuss. I then provide a case study of a qubit in a bath of spin 1/2 particles, for which the reachability question can be solved analytically, and provide numerical results using an open-source software library developed by our group.