  We show that it is possible to reduce the number of two-qubit gates needed
for the construction of an arbitrary controlled-unitary transformation by up to
two times using a tunable controlled-phase gate. On the platform of linear
optics, where two-qubit gates can only be achieved probabilistically, our
method significantly reduces the amount of components and increases success
probability of a two-qubit gate. The experimental implementation of our
technique presented in this paper for a controlled single-qubit unitary gate
demonstrates that only one tunable controlled-phase gate is needed instead of
two standard controlled-NOT gates. Thus, not only do we increase success
probability by about one order of magnitude (with the same resources), but also
avoid the need for conducting quantum non-demolition measurement otherwise
required to join two probabilistic gates. Subsequently, we generalize our
method to a higher order, showing that n-times controlled gates can be
optimized by replacing blocks of controlled-NOT gates with tunable
controlled-phase gates.
