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

TL;DR

This study demonstrates that vanadyl porphyrin molecules can serve as multi-level quantum systems, or qudits, with long coherence times and tunable properties suitable for quantum computing and error correction.

Contribution

The paper introduces vanadyl porphyrin molecules as viable multi-qubit and qudit quantum systems with detailed spectroscopic characterization and potential for quantum information processing.

Findings

Spin coherence times of microseconds at low temperatures.

Long spin relaxation times exceeding one second.

Ability to operate as a 4-qubit processor or d=16 qudit under certain conditions.

Abstract

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.