Broad-band spectroscopy of a vanadyl porphyrin: a model electronuclear spin qudit

• Published in: Chemical science (Cambridge) Vol. 12; no. 15; pp. 5621 - 563
• Main Authors: Gimeno, Ignacio, Urtizberea, Ainhoa, Román-Roche, Juan, Zueco, David, Camón, Agustín, Alonso, Pablo J, Roubeau, Olivier, Luis, Fernando
• Format: Journal Article
• Language: English
• Published: Cambridge Royal Society of Chemistry 21.04.2021; The Royal Society of Chemistry
• Subjects: Chemistry; Crystallography; Electron paramagnetic resonance; Electron spin; Energy levels; Error correction; Low temperature; Magnetic fields; Magnetic spectroscopy; Microprocessors; Nuclear spin; Quantum entanglement; Qubits (quantum computing); Rabi frequency; Single crystals; Specific heat; Spectrum analysis; Spin dynamics; Vanadyl porphyrins
• ISSN: 2041-6520; 2041-6539
• DOI: 10.1039/d1sc00564b

We explore how to encode more than a qubit in vanadyl porphyrin molecules hosting a S = 1/2 electronic spin coupled to a I = 7/2 nuclear spin. 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 > 0.1 T, corresponding to resonance frequencies of 9-10 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 '1' and '0' basis states. For lower magnetic fields ( B < 0.1 T), and lower frequencies (<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. We show that a sizeable electronuclear entanglement of the S = 1/2 and I = 7/2 spins of a vanadyl porphyrin provides the conditions to act as a universal 4-qubit processor, and thus implement quantum error correction at the molecular level.