  One of the essential building blocks of classical computer programs is the
"if" clause, which executes a subroutine depending on the value of a control
variable. Similarly, several quantum algorithms rely on applying a unitary
operation conditioned on the state of a control system. Here we show that this
control cannot be performed by a quantum circuit if the unitary is completely
unknown. However, this no-go theorem does not prevent implementing quantum
control of unknown unitaries in practice, as any physical implementation of an
unknown unitary provides additional information that makes the control
possible. We then argue that one should extend the quantum circuit formalism to
capture this possibility in a straightforward way. This is done by allowing
unknown unitaries to be applied to subspaces and not only to subsystems.
