Quantum logic gates are the crucial information-processing operation of quantum
computers. Two crucial performance metrics for logic gates are their precision and
speed. Quantum processors based on trapped ions have always been the touchstone
for gate precision, but have suffered from slow speed relative to other quantum logic
platforms such as solid state systems. This thesis shows that it is possible to accelerate
the logic "clock speed" from kHz to MHz speeds, whilst maintaining a precision of
99.8%. This is almost as high as the world record for conventional trapped-ion gates,
but more than 20 times faster. It also demonstrates entanglement generation in a
time (480ns) shorter than the natural timescale of the ions' motion in the trap, which
starts to probe an interesting new regime of ion trap physics.
In separate experiments, some of the first "mixed-species" quantum logic gates are
performed, both between two different elements, and between different isotopes.
The mixed-isotope gate is used to make the first test of the quantum-mechanical Bell
inequality between two different species of isolated atoms.