  The optimally designed control of quantum systems is playing an increasingly
important role to engineer novel and more efficient quantum technologies. Here,
in the scenario represented by controlling an arbitrary quantum system via the
interaction with an another optimally initialized auxiliary quantum system, we
show that the quantum channel capacity sets the scaling behaviour of the
optimal control error. Specifically, we prove that the minimum control error is
ensured by maximizing the quantum capacity of the channel mapping the initial
control state into the target state of the controlled system, i.e., optimizing
the quantum information flow from the controller to the system to be
controlled. Analytical results, supported by numerical evidences, are provided
when the systems and the controller are either qubits or single Bosonic modes
and can be applied to a very large class of platforms for controllable quantum
devices.
