  Control over physical systems at the quantum level is a goal shared by
scientists in fields as diverse as metrology, information processing,
simulation and chemistry. For trapped atomic ions, the quantized motional and
internal degrees of freedom can be coherently manipulated with laser light.
Similar control is difficult to achieve with radio frequency or microwave
radiation because the essential coupling between internal degrees of freedom
and motion requires significant field changes over the extent of the atoms'
motion. The field gradients are negligible at these frequencies for freely
propagating fields; however, stronger gradients can be generated in the
near-field of microwave currents in structures smaller than the free-space
wavelength. In the experiments reported here, we coherently manipulate the
internal quantum states of the ions on time scales of 20 ns. We also generate
entanglement between the internal degrees of freedom of two atoms with a gate
operation suitable for general quantum computation. We implement both
operations through the magnetic fields from microwave currents in electrodes
that are integrated into the micro-fabricated trap structure and create an
entangled state with fidelity 76(3) %. This approach, where the quantum control
mechanism is integrated into the trapping device in a scalable manner, can
potentially benefit quantum information processing, simulation and
spectroscopy.
