  It is well known that a universal set of gates for classical computation
augmented with the Hadamard gate results in universal quantum computing. While
this requires the addition of a genuine quantum element to the set of passive
classical gates, here we ask the following: can the same result be attained by
adding a quantum control unit while keeping the circuit itself completely
classical? In other words, can we get universal quantum computation by
coherently controlling classical operations? In this work we provide an
affirmative answer to this question, by considering a computational model that
consists of $2n$ target bits together with a set of classical gates, controlled
by log$(2n+1)$ ancillary qubits. We show that this model is equivalent to a
quantum computer operating on $n$ qubits. Furthermore, we show that even a
primitive computer that is capable of implementing only SWAP gates, can be
lifted to universal quantum computing, if aided with an appropriate quantum
control of logarithmic size. Our results thus exemplify the information
processing power brought forth by the quantum control system.
