  A promising platform for quantum information processing is that of silicon
impurities, where the quantum states are manipulated by magnetic resonance.
Such systems, in abstraction, can be considered as a nucleus of arbitrary spin
coupled to an electron of spin one-half via an isotropic hyperfine interaction.
We therefore refer to them as "nuclear-electronic spin systems". The
traditional example, being subject to intensive experimental studies, is that
of phosphorus doped silicon (Si:P) which couples a spin one-half electron to a
nucleus of the same spin, with a hyperfine strength of 117.5 MHz. More
recently, bismuth doped silicon (Si:Bi) has been suggested as an alternative
instantiation of nuclear-electronic spin systems, differing from Si:P by its
larger nuclear spin and hyperfine strength of 9/2 and 1.4754 GHz respectively.
The aim of this thesis has been to develop a model that is capable of
predicting the magnetic resonance properties of nuclear-electronic spin
systems. The theoretical predictions of this model have been tested against
experimental data collected on Si:Bi at 4.044 GHz, and have proven quite
successful. Furthermore, the larger nuclear spin and hyperfine strength of
Si:Bi, compared with that of Si:P, are predicted to offer advantages for
quantum information processing. Most notable amongst these is that magnetic
field-dependent two-dimensional decoherence free subspaces, called optimal
working points, have been identified to exist in Si:Bi, but not Si:P.
