  The interaction between Rydberg states of neutral atoms is strong and
long-range, making it appealing to put it to use in the context of quantum
technologies. Recently, first applications of this idea have been reported in
the fields of quantum computation and quantum simulation. Furthermore,
electromagnetically induced transparency allows to map these Rydberg
interactions to light. Here we exploit this mapping and the resulting
interaction between photons to realize a photon-photon quantum gate,
demonstrating the potential of Rydberg systems as a platform also for quantum
communication and quantum networking. We measure a controlled-NOT truth table
with a fidelity of 70(8)% and an entangling-gate fidelity of 63.7(4.5)%, both
post-selected upon detection of a control and a target photon. The level of
control reached here is an encouraging step towards exploring novel many-body
states of photons or for future applications in quantum communication and
quantum networking.
