  We demonstrate universal quantum control over chains of ions in a
surface-electrode ion trap, including all the fundamental operations necessary
to perform algorithms in a one-dimensional, nearest-neighbor quantum computing
architecture. We realize both single-qubit operations and nearest-neighbor
entangling gates with Raman laser beams, and we interleave the two gate types.
We report average single-qubit gate fidelities as high as 0.970(1) for two-,
three-, and four-ion chains, characterized with randomized benchmarking. We
generate Bell states between the nearest-neighbor pairs of a three-ion chain,
with fidelity up to 0.84(2). We combine one- and two-qubit gates to perform
quantum process tomography of a CNOT gate in a two-ion chain, and we report an
overall fidelity of 0.76(3).
