  We consider a scenario where we wish to bring a closed system of known
Hilbert space dimension $d_S$ (the target), subject to an unknown Hamiltonian
evolution, back to its quantum state at a past time $t_0$. The target is out of
our control: this means that we ignore both its free Hamiltonian and how the
system interacts with other quantum systems we may use to influence it. Under
these conditions, we prove that there exist protocols within the framework of
non-relativistic quantum physics which reset the target system to its exact
quantum state at $t_0$. Each "resetting protocol" is successful with non-zero
probability for all possible free Hamiltonians and interaction unitaries, save
a subset of zero measure. When the target is a qubit and the interaction is
sampled from the Haar measure, the simplest resetting circuits have a
significant average probability of success and their implementation is within
reach of current quantum technologies. Finally, we find that, in case the
resetting protocol fails, it is possible to run a further protocol that, if
successful, undoes both the natural evolution of the target and the effects of
the failed protocol over the latter. By chaining in this fashion several such
protocols, one can substantially increase the overall probability of a
successful resetting.
