  We study reachable sets of open n-qubit quantum systems, whose coherent parts
are under full unitary control, by adding as a further degree of incoherent
control switchable Markovian noise on a single qubit. In particular, adding
bang-bang control of amplitude damping noise (non-unital) allows the dynamic
system to act transitively on the entire set of density operators. Thus one can
transform any initial quantum state into any desired target state. Adding
switchable bit-flip noise (unital) instead suffices to get all states majorised
by the initial state. Our open-loop optimal control package DYNAMO is extended
by incoherent control to exploit these unprecedented reachable sets in
experiments. We propose implementation by a GMon, a superconducting device with
fast tunable coupling to an open transmission line, and illustrate how
open-loop control with noise switching achieves all state transfers without
measurement-based closed-loop feedback and resettable ancilla.
