  The long coherence times and strong Coulomb interactions afforded by trapped
ion qubits have enabled realizations of the necessary primitives for quantum
information processing (QIP), and indeed the highest-fidelity quantum
operations in any qubit to date. But while light delivery to each individual
ion in a system is essential for general quantum manipulations and readout,
experiments so far have employed optical systems cumbersome to scale to even a
few tens of qubits. Here we demonstrate lithographically defined nanophotonic
waveguide devices for light routing and ion addressing fully integrated within
a surface-electrode ion trap chip. Ion qubits are addressed at multiple
locations via focusing grating couplers emitting through openings in the trap
electrodes to ions trapped 50 $\mu$m above the chip; using this light we
perform quantum coherent operations on the optical qubit transition in
individual $^{88}$Sr$^+$ ions. The grating focuses the beam to a
diffraction-limited spot near the ion position with a 2 $\mu$m 1/$e^2$-radius
along the trap axis, and we measure crosstalk errors between $10^{-2}$ and
$4\times10^{-4}$ at distances 7.5-15 $\mu$m from the beam center. Owing to the
scalability of the planar fabrication employed, together with the tight
focusing and stable alignment afforded by optics integration within the trap
chip, this approach presents a path to creating the optical systems required
for large-scale trapped-ion QIP.
