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

Molecular nanomagnets: a viable path toward quantum information processing?

Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.

Magnetic Relaxations of Chromium Nitride Porphyrinato Complexes Driven by the Anisotropic g-Factor

Molecule-based magnetic materials are useful candidates as the spin qubit due to their long coherence time and high designability. The anisotropy of the g-values of the metal complexes can be utilized to access the individual spin of the metal complexes, making it possible to achieve the scalable molecular spin qubit. For this goal, it is important to evaluate the effect of g-value anisotropy on the magnetic relaxation behaviour. This study reports the slow magnetic relaxation behaviour of chromium nitride (CrN2+ ) porphyrinato complex (1), which is structurally and magnetically similar with the vanadyl (VO2+ ) porphyrinato complex (2) which is known as the excellent spin qubit. Detailed analyses for vibrational and dynamical magnetism of 1 and 2 revealed that g-value anisotropy accelerates magnetic relaxations greater than the internal magnetic field from nuclear spin does. These results provide a design criterion for construction of multiple spin qubit based on g-tensor engineering.

Quantum spin coherence and electron spin distribution channels in vanadyl-containing lantern complexes

We herein investigate the heterobimetallic lantern complexes [PtVO(SOCR)4] as charge neutral electronic qubits based on vanadyl complexes (S = 1/2) with nuclear spin-free donor atoms. The derivatives with R = Me (1) and Ph (2) give highly resolved X-band EPR spectra in frozen CH2Cl2/toluene solution, which evidence the usual hyperfine coupling with the 51V nucleus (I = 7/2) and an additional superhyperfine interaction with the I = 1/2 nucleus of the 195Pt isotope (natural abundance ca. 34%). DFT calculations ascribe the spin density delocalization on the Pt2+ ion to a combination of π and δ pathways, with the former representing the predominant channel. Spin relaxation measurements in frozen CD2Cl2/toluene-d8 solution between 90 and 10 K yield Tm values (1-6 μs in 1 and 2-11 μs in 2) which compare favorably with those of known vanadyl-based qubits in similar matrices. Coherent spin manipulations indeed prove possible at 70 K, as shown by the observation of Rabi oscillations in nutation experiments. The results indicate that the heavy Group 10 metal ion is not detrimental to the coherence properties of the vanadyl moiety and that Pt-VO lanterns can be used as robust spin-coherent building blocks in materials science and quantum technologies.

Dilute Gd hydroxycarbonate particles for localized spin qubit integration

Molecular spins are considered as the quantum hardware to build hybrid quantum processors in which coupling to superconducting devices would provide the means to implement the necessary coherent manipulations. As an alternative to large magnetically-dilute crystals or concentrated nano-scale deposits of paramagnetic molecules that have been studied so far, the use of pre-formed sub-micronic spherical particles of a doped Gd@Y hydroxycarbonate is evaluated here. Particles with an adjustable number of spin carriers are prepared through the control of both particle size and doping. Bulk magnetic properties and continuous wave and time-domain-EPR spectroscopy show that the Gd spins in these particles are potential qubits with robust quantum coherence. Monolayers of densely-packed particles are then formed interfacially and transferred successfully to the surface of Nb superconducting resonators. Alternatively, these particles are disposed at controlled localizations as isolated groups of a few particles through Dip-Pen Nanolithography using colloidal organic dispersions as ink. Altogether, this study offers new material and methodologies relevant to the development of viable hybrid quantum processors.

A Review of the Current State of Magnetic Force Microscopy to Unravel the Magnetic Properties of Nanomaterials Applied in Biological Systems and Future Directions for Quantum Technologies

Magnetism plays a pivotal role in many biological systems. However, the intensity of the magnetic forces exerted between magnetic bodies is usually low, which demands the development of ultra-sensitivity tools for proper sensing. In this framework, magnetic force microscopy (MFM) offers excellent lateral resolution and the possibility of conducting single-molecule studies like other single-probe microscopy (SPM) techniques. This comprehensive review attempts to describe the paramount importance of magnetic forces for biological applications by highlighting MFM's main advantages but also intrinsic limitations. While the working principles are described in depth, the article also focuses on novel micro- and nanofabrication procedures for MFM tips, which enhance the magnetic response signal of tested biomaterials compared to commercial nanoprobes. This work also depicts some relevant examples where MFM can quantitatively assess the magnetic performance of nanomaterials involved in biological systems, including magnetotactic bacteria, cryptochrome flavoproteins, and magnetic nanoparticles that can interact with animal tissues. Additionally, the most promising perspectives in this field are highlighted to make the reader aware of upcoming challenges when aiming toward quantum technologies.

How to Cross an Energy Barrier at Zero Kelvin without Tunneling Effect

This Letter deals with the broad class of magnetic systems having a single or collective spin S with an energy barrier, such as rare-earth elements and their compounds, single molecule magnets with uniaxial anisotropy, and more generally any other anisotropic quantum system made of single or multiple objects with discrete energy levels. Till now, the reversal of the magnetization of such systems at zero kelvin required making use of quantum tunneling with a significant transverse field or transverse anisotropy term, at resonance. Here, we show that another very simple method exists. It simply consists in the application of a particular sequence of electromagnetic radiations in the ranges of optical or microwave frequencies, depending on the characteristics of the system (spin and anisotropy values for magnetic systems). This produces oscillations of the Rabi type that pass above the barrier, thus extending these oscillations between the two energy wells with mixtures of all the 2S+1 states. In addition to its basic character, this approach opens up new directions of research in quantum information with possible breakthroughs in the current use of multiple quantum bits.

The critical role of ultra-low-energy vibrations in the relaxation dynamics of molecular qubits

Improving the performance of molecular qubits is a fundamental milestone towards unleashing the power of molecular magnetism in the second quantum revolution. Taming spin relaxation and decoherence due to vibrations is crucial to reach this milestone, but this is hindered by our lack of understanding on the nature of vibrations and their coupling to spins. Here we propose a synergistic approach to study a prototypical molecular qubit. It combines inelastic X-ray scattering to measure phonon dispersions along the main symmetry directions of the crystal and spin dynamics simulations based on DFT. We show that the canonical Debye picture of lattice dynamics breaks down and that intra-molecular vibrations with very-low energies of 1-2 meV are largely responsible for spin relaxation up to ambient temperature. We identify the origin of these modes, thus providing a rationale for improving spin coherence. The power and flexibility of our approach open new avenues for the investigation of magnetic molecules with the potential of removing roadblocks toward their use in quantum devices.

Quantum Mimicry With Inorganic Chemistry

Quantum objects, such as atoms, spins, and subatomic particles, have important properties due to their unique physical properties that could be useful for many different applications, ranging from quantum information processing to magnetic resonance imaging. Molecular species also exhibit quantum properties, and these properties are fundamentally tunable by synthetic design, unlike ions isolated in a quadrupolar trap, for example. In this comment, we collect multiple, distinct, scientific efforts into an emergent field that is devoted to designing molecules that mimic the quantum properties of objects like trapped atoms or defects in solids. Mimicry is endemic in inorganic chemistry and featured heavily in the research interests of groups across the world. We describe a new field of using inorganic chemistry to design molecules that mimic the quantum properties (e.g. the lifetime of spin superpositions, or the resonant frequencies thereof) of other quantum objects, "quantum mimicry." In this comment, we describe the philosophical design strategies and recent exciting results from application of these strategies.

Dipolar-Coupled Entangled Molecular 4f Qubits

We demonstrate by use of continuous wave- and pulse-electron paramagnetic resonance spectroscopy on oriented single crystals of magnetically dilute Yb^III ions in Yb_0.01Lu_0.99(trensal) that molecular entangled two-qubit systems can be constructed by exploiting dipolar interactions between neighboring Yb^III centers. Furthermore, we show that the phase memory time and Rabi frequencies of these dipolar-interaction-coupled entangled two-qubit systems are comparable to the ones of the corresponding single qubits.

An exchange coupled meso-meso linked vanadyl porphyrin dimer for quantum information processing

We report here the synthesis of a new meso-meso (m-m) singly linked vanadyl-porphyrin dimer that crystallizes in two different pseudo-polymorphs. The single crystal continuous-wave electron paramagnetic resonance investigation evidences a small but crucial isotropic exchange interaction, J, between the two tilted, and thus distinguishable, spin centers of the order of 10^-2 cm^-1. The experimental and DFT studies evidence a correlation between J values and porphyrin plane tilting angle and distortion. Pulsed EPR analysis shows that the two vanadyl dimers maintain the coherence time of the monomer. With the obtained spin Hamiltonian parameters, we identify suitable transitions that could be used as computational basis states. Our results, coupled with the evaporability of porphyrin systems, establish this class of dimers as extremely promising for quantum information processing applications.

Theoretical Design of Optimal Molecular Qudits for Quantum Error Correction

We pinpoint the key ingredients ruling decoherence in multispin clusters, and we engineer the system Hamiltonian to design optimal molecules embedding quantum error correction. These are antiferromagnetically coupled systems with competing exchange interactions, characterized by many low-energy states in which decoherence is dramatically suppressed and does not increase with the system size. This feature allows us to derive optimized code words, enhancing the power of the quantum error correction code by orders of magnitude. We demonstrate this by a complete simulation of the system dynamics, including the effect of decoherence driven by a nuclear spin bath and the full sequence of pulses to implement error correction and logical gates between protected states.

Magnetic interaction of photoexcited terbium-porphyrin complexes with non-aromatic ligands having different symmetries

Interaction between the total angular momentum (J) of 4f electrons in lanthanides and the orbital angular momentum (L) of porphyrins in the photoexcited states was investigated by temperature-dependent and magnetic circular dichroism (MCD) for 5,10,15,20-tetraphenylporphyrinato (TPP) terbium(III) complexes with two different non-aromatic ligands i.e. 12-crown-4(1,4,7,10-tetraoxacyclododecane) and 1-aza-12-crown-4(1,4,7-trioxa-10-azacyclododecane). The two cases with different ligands were examined in order to understand how magnetic interaction depends on the symmetry of the non-aromatic ligands. The three absorption bands in the visible region, B(0,0), Q(1,0), and Q(0,0) bands, showed temperature-dependent MCD A term. For each band, the J-L interaction was determined from the simulation-based fitting to experimental ratios. An increase in the magnitude of the J-L interaction was observed when the second ligand was the aza-crown with a lower symmetry. Ab initio RASSCF/RASSI calculations were performed to explore the effect of the difference in the second ligand to the ligand centred excited states and the ligand-field-splitting structure on the metal-centred ground multiplet of J = 6.

Solid polymorphism and dynamic magnetic properties of a dodecylated vanadyl–porphyrinato complex: spin–lattice relaxations modulated by phase stabilisation

Phase stabilisation elongates spin–lattice relaxation times.

Controlled coherent dynamics of [VO(TPP)], a prototype molecular nuclear qudit with an electronic ancilla

We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising system to implement quantum computation algorithms based on encoding information in multi-level (qudit) units. Indeed, it embeds a nuclear spin 7/2 coupled to an electronic spin 1/2 by hyperfine interaction. This qubit-qudit unit can be exploited to implement quantum error correction and quantum simulation algorithms. Through a combined theoretical and broadband nuclear magnetic resonance study, we demonstrate that the elementary operations of such algorithms can be efficiently implemented on the nuclear spin qudit. Manipulation of the nuclear qudit can be achieved by resonant radio-frequency pulses, thanks to the remarkably long coherence times and the effective quadrupolar coupling induced by the strong hyperfine interaction. This approach may open new perspectives for developing new molecular qubit-qudit systems.

Radiofrequency to Microwave Coherent Manipulation of an Organometallic Electronic Spin Qubit Coupled to a Nuclear Qudit

We report here a comprehensive characterization of a 3d organometallic complex, [V(Cp)2Cl2] (Cp = cyclopentadienyl), which can be considered as a prototypical multilevel nuclear qudit (nuclear spin I = 7/2) hyperfine coupled to an electronic qubit (electronic spin S = 1/2). By combining complementary magnetic resonant techniques, such as pulsed electron paramagnetic resonance (EPR) and broadband nuclear magnetic resonance (NMR), we extensively characterize its Spin Hamiltonian parameters and its electronic and nuclear spin dynamics. Moreover, we demonstrate the possibility to manipulate the qubit-qudit multilevel structure by resonant microwave and radiofrequency pulses, driving coherent Rabi oscillations between targeted electronuclear states. The obtained results demonstrate that this simple complex is a promising candidate for quantum computing applications.