Broad-band spectroscopy of electronuclear spin qudits based on vanadyl porphyrin molecules

The possibility of encoding several qubits in vanadyl porphyrin molecules hosting a S = 1/2 electronic spin coupled to a I = 7/2 nuclear spin has been explored. A complete study of the spin Hamiltonian and the spin dynamics has been performed via a combination of electron paramagnetic resonance, heat capacity, magnetization and on-chip magnetic spectroscopy experiments performed on single crystals, observing low temperature T₂ of micro-seconds and T₁ longer than a second. For sufficiently strong magnetic fields (B > 0.1 T, corresponding to resonance frequencies of 9–10 GHz) these properties make vanadyl porphyrin molecules suitable qubit realizations. For lower magnetic fields (B < 0.1 T), and lower frequencies (< 2 GHz), spectroscopic signatures of a sizeable electronuclear entanglement arise. This effect generates a larger set of allowed transitions between different electronuclear spin states and removes their degeneracies. Under these conditions, each molecule fulfils 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 quantum error correction at the molecular level.