  We present a study of the prospects for coherence preservation in solid-state
spin qubits using dynamical decoupling protocols. Recent experiments have
provided the first demonstrations of multipulse dynamical decoupling sequences
in this qubit system, but quantitative analyses of potential coherence
improvements have been hampered by a lack of concrete knowledge of the relevant
noise processes. We present simulations of qubit coherence under the
application of arbitrary dynamical decoupling pulse sequences based on an
experimentally validated semiclassical model. This phenomenological approach
bundles the details of underlying noise processes into a single experimentally
relevant noise power spectral density. Our results show that the dominant
features of experimental measurements in a two-electron singlet-triplet spin
qubit can be replicated using a $1/\omega^{2}$ noise power spectrum associated
with nuclear-spin-flips in the host material. Beginning with this validation we
address the effects of nuclear programming, high-frequency nuclear-spin
dynamics, and other high-frequency classical noise sources, with conjectures
supported by physical arguments and microscopic calculations where relevant.
Our results provide expected performance bounds and identify diagnostic metrics
that can be measured experimentally in order to better elucidate the underlying
nuclear spin dynamics.
