  Quantum bits based on individual trapped atomic ions constitute a promising
technology for building a quantum computer, with all the elementary operations
having been achieved with the necessary precision for some error-correction
schemes. However, the essential two-qubit logic gate used for generating
quantum entanglement has hitherto always been performed in an adiabatic regime,
where the gate is slow compared with the characteristic motional frequencies of
ions in the trap, giving logic speeds of order 10kHz. There have been numerous
proposals for performing gates faster than this natural "speed limit" of the
trap. We implement the method of Steane et al., which uses tailored laser
pulses: these are shaped on 10 ns timescales to drive the ions' motion along
trajectories designed such that the gate operation is insensitive to optical
phase fluctuations. This permits fast (MHz-rate) quantum logic which is robust
to this important source of experimental error. We demonstrate entanglement
generation for gate times as short as 480ns; this is less than a single
oscillation period of an ion in the trap, and 8 orders of magnitude shorter
than the memory coherence time measured in similar calcium-43 hyperfine qubits.
The method's power is most evident at intermediate timescales, where it yields
a gate error more than ten times lower than conventional techniques; for
example, we achieve a 1.6 us gate with fidelity 99.8%. Still faster gates are
possible at the price of higher laser intensity. The method requires only a
single amplitude-shaped pulse and one pair of beams derived from a
continuous-wave laser, and offers the prospect of combining the unrivalled
coherence properties, operation fidelities and optical connectivity of
trapped-ion qubits with the sub-microsecond logic speeds usually associated
with solid state devices.
