  The flip-flop qubit, encoded in the states with antiparallel donor-bound
electron and donor nuclear spins in silicon, showcases long coherence times,
good controllability, and, in contrast to other donor-spin-based schemes,
long-distance coupling. Electron spin control near the interface, however, is
likely to shorten the relaxation time by many orders of magnitude, reducing the
overall qubit quality factor. Here, we theoretically study the multilevel
system that is formed by the interacting electron and nuclear spins and derive
analytical effective two-level Hamiltonians with and without periodic driving.
We then propose an optimal control scheme that produces fast and robust
single-qubit gates in the presence of low-frequency noise and relatively weak
magnetic fields without relying on parametrically restrictive sweet spots. This
scheme increases considerably both the relaxation time and the qubit quality
factor.
