  Impurities hosted in semiconducting solid matrices represent an extensively
studied platform for quantum computing applications. In this scenario, the
so-called flip-flop qubit emerges as a convenient choice for scalable
implementations in silicon. Flip-flop qubits are realized implanting
phosphorous donor in isotopically purified silicon, and encoding the logical
states in the donor nuclear spin and in its bound electron. Electrically
modulating the hyperfine interaction by applying a vertical electric field
causes an Electron Dipole Spin Resonance (EDSR) transition between the states
with antiparallel spins
$\{|\downarrow\Uparrow\rangle,|\uparrow\Downarrow\rangle\}$, that are chosen as
the logical states. When two qubits are considered, the dipole-dipole
interaction is exploited allowing long-range coupling between them. A universal
set of quantum gates for flip-flop qubits is here proposed and the effect of a
realistic 1/f noise on the gate fidelity is investigated for the single qubit
$R_z(-\frac{\pi}{2})$ and Hadamard gate and for the two-qubit $\sqrt{iSWAP}$
gate.
