  We have analyzed effects of the hyperfine interaction on electric dipole spin
resonance when the amplitude of the quantum-dot motion becomes comparable or
larger than the quantum dot's size. Away from the well known small-drive
regime, the important role played by transverse nuclear fluctuations leads to a
gaussian decay with characteristic dependence on drive strength and detuning. A
characterization of spin-flip gate fidelity, in the presence of such additional
drive-dependent dephasing, shows that vanishingly small errors can still be
achieved at sufficiently large amplitudes. Based on our theory, we analyze
recent electric-dipole spin resonance experiments relying on spin-orbit
interactions or the slanting field of a micromagnet. We find that such
experiments are already in a regime with significant effects of transverse
nuclear fluctuations and the form of decay of the Rabi oscillations can be
reproduced well by our theory.
