  We explore how to encode more than a qubit in vanadyl porphyrin molecules
hosting a electronic spin 1/2 coupled to a nuclear spin 7/2. The spin
Hamiltonian and its parameters, as well as the spin dynamics, have been
determined via a combination of electron paramagnetic resonance, heat capacity,
magnetization and on-chip magnetic spectroscopy experiments performed on single
crystals. We find low temperature spin coherence times of micro-seconds and
spin relaxation times longer than a second. For sufficiently strong magnetic
fields (B larger than 0.1 T, corresponding to resonance frequencies of 9 to 10
GHz) these properties make vanadyl porphyrin molecules suitable qubit
realizations. The presence of multiple equispaced nuclear spin levels then
merely provides 8 alternatives to define the 0 and 1 basis states. For lower
magnetic fields (below 0.1 T), and lower frequencies (smaller than 2 GHz), we
find spectroscopic signatures of a sizeable electronuclear entanglement. This
effect generates a larger set of allowed transitions between different
electronuclear spin states and removes their degeneracies. Under these
conditions, we show that each molecule fulfills the conditions to act as a
universal 4-qubit processor or, equivalently, as a d = 16 qudit. These findings
widen the catalogue of chemically designed systems able to implement
non-trivial quantum functionalities, such as quantum simulations and,
especially, quantum error correction at the molecular level.
