This thesis describes experimental work in which the spin and motional states of
one and two trapped atomic ions are manipulated with long-wavelength radiation in
the microwave and radio frequency (RF) regime. This allows single- and two-qubit
quantum logic gates to be implemented with long-wavelength radiation, in contrast
to laser frequency radiation used in the majority of work to date. The two-qubit gate
scheme developed represents a significant advance towards a large scale quantum
computing architecture in which laser light is not needed for coherent manipulation.
An experimental setup is built in which a macroscopic linear Paul trap is fitted
with permanent magnets to create a strong axial magnetic field gradient. This
addition allows the spin and motional states of the ions to be coupled using long-wavelength
radiation. The coherence time of qubits that are sensitive to the magnetic
field gradient is increased by nearly three orders of magnitude with the use of dressed
states and the lifetime and coherence time are measured to be T1 = 0.63(4) s and
T2 = 0.65(5) s, respectively. Using the dressed-state qubit, sideband cooling of a
single ion to the motional ground state is demonstrated, and the final mean phonon
number after cooling is measured to be \bar{n} = 0.13(4). Finally, a two-qubit gate is
demonstrated using the dressed-state qubits in conjunction with the magnetic field
gradient, and a Bell state fidelity of F = 0.985(12) is determined. This is a
significant increase in fidelity for a two-qubit gate based on long-wavelength radiation
compared to previous work. The errors are analysed and it is shown that with the
next generation of microfabricated traps being developed in the group, the gate
fidelity using this scheme can be pushed far into the fault tolerant regime. This
makes this scheme promising as an integral part of a large scale quantum computing
architecture.