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

Schematic drawing of the experimental setup. The components are labeled as follows: MT—motorized translation, HWP—half-wave plate, QWP—quarter-wave plate, PBS—polarizing beam splitter, BDA—beam divider assembly, BD—beam divider, F—neutral density filter, D—detector.

¹RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Academy of Sciences of the Czech Republic, 17. listopadu 12, 771 46 Olomouc, Czech Republic
²Faculty of Physics, Adam Mickiewicz University, PL-61-614 Poznań, Poland
³Institute of Physics of Academy of Sciences of the Czech Republic, Joint Laboratory of Optics of PU and IP AS CR, 17. listopadu 50A, 772 07 Olomouc, Czech Republic
⁴Department of Optics, Faculty of Science, Palacký University, 17. listopadu 12, cz-77146 Olomouc, Czech Republic