  We demonstrate, numerically, the possibility of manipulating the spin states
of molecular nanomagnets with shaped microwave pulses designed with quantum
optimal control theory techniques. The state-to-state or full gate
transformations can be performed in this way in shorter times than using simple
monochromatic resonant pulses. This enhancement in the operation rates can
therefore mitigate the effect of decoherence. The optimization protocols and
their potential for practical implementations are illustrated by simulations
performed for a simple molecular cluster hosting a single Gd$^{3+}$ ion. Its
eight accessible levels (corresponding to a total spin $S=7/2$) allow encoding
an $8$-level qudit or a system of three coupled qubits. All necessary gates
required for universal operation can be obtained with optimal pulses using the
intrinsic couplings present in this system. The application of optimal control
techniques can facilitate the implementation of quantum technologies based on
molecular spin qudits.
