Experimental Implementation of Optimal Linear-Optical Controlled-Unitary Gates

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 2 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 Letter 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 the success probability by about 1 order of magnitude (with the same resources), but also avoid the need for conducting quantum nondemolition 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.