  Networks of Rydberg atoms provide a powerful basis for quantum simulators and
quantum technologies. Inspired by matter-wave atomtronics, here we engineer
switches, diodes and universal logic gates. Our schemes control the Rydberg
excitation dynamics via the anti-blockade or facilitation mechanism, allowing
for much faster devices compared to cold atom systems. Our approach is robust
to noise and can be applied to individually trapped atoms and extensive
three-dimensional gases. In analogy to electronics, Rydberg atomtronic devices
promise to enhance quantum information processors and quantum simulators.
