  Trapped Rydberg ions are a promising novel approach to quantum computing and
simulations. They are envisaged to combine the exquisite control of trapped ion
qubits with the fast two-qubit Rydberg gates already demonstrated in neutral
atom experiments. Coherent Rydberg excitation is a key requirement for these
gates. Here, we carry out the first coherent Rydberg excitation of an ion and
perform a single-qubit Rydberg gate, thus demonstrating basic elements of a
trapped Rydberg ion quantum computer.
