  We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising
system suitable to implement quantum computation algorithms based on encoding
information in multi-level (qudit) units. Indeed, it embeds an electronic spin
1/2 coupled through hyperfine interaction to a nuclear spin 7/2, both
characterized by remarkable coherence. We demonstrate this by an extensive
broadband nuclear magnetic resonance study, which allow us to characterize the
nuclear spin-Hamiltonian and to measure the spin dephasing time as a function
of the magnetic field. In addition, we combine targeted measurements and
numerical simulations to show that nuclear spin transitions conditioned by the
state of the electronic qubit can be individually addressed and coherently
manipulated by resonant radio-frequency pulses, thanks to the remarkably long
coherence times and the effective quadrupolar coupling induced by the strong
hyperfine coupling. This approach may open new perspectives for developing new
molecular qubit-qudit systems.
