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.

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.

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.

Assessing the Nature of Chiral-Induced Spin Selectivity by Magnetic Resonance.

Understanding chiral-induced spin selectivity (CISS), resulting from charge transport through helical systems, has recently inspired many experimental and theoretical efforts but is still the object of intense debate. In order to assess the nature of CISS, we propose to focus on electron-transfer processes occurring at the single-molecule level. We design simple magnetic resonance experiments, exploiting a qubit as a highly sensitive and coherent magnetic sensor, to provide clear signatures of the acceptor polarization. Moreover, we show that information could even be obtained from time-resolved electron paramagnetic resonance experiments on a randomly oriented solution of molecules. The proposed experiments will unveil the role of chiral linkers in electron transfer and could also be exploited for quantum computing applications.

Erratum: Many-Body Models for Molecular Nanomagnets [Phys. Rev. Lett. 110, 157204 (2013)].

This corrects the article DOI: 10.1103/PhysRevLett.110.157204.

Molecular Nanomagnets as Qubits with Embedded Quantum-Error Correction.

We show that molecular nanomagnets have a potential advantage in the crucial rush toward quantum computers. Indeed, the sizable number of accessible low-energy states of these systems can be exploited to define qubits with embedded quantum error correction. We derive the scheme to achieve this crucial objective and the corresponding sequence of microwave/radiofrequency pulses needed for the error correction procedure. The effectiveness of our approach is shown already with a minimal S = 3/2 unit corresponding to an existing molecule, and the scaling to larger spin systems is quantitatively analyzed.

Unveiling phonons in a molecular qubit with four-dimensional inelastic neutron scattering and density functional theory.

Phonons are the main source of relaxation in molecular nanomagnets, and different mechanisms have been proposed in order to explain the wealth of experimental findings. However, very limited experimental investigations on phonons in these systems have been performed so far, yielding no information about their dispersions. Here we exploit state-of-the-art single-crystal inelastic neutron scattering to directly measure for the first time phonon dispersions in a prototypical molecular qubit. Both acoustic and optical branches are detected in crystals of [VO(acac)[Formula: see text]] along different directions in the reciprocal space. Using energies and polarisation vectors calculated with state-of-the-art Density Functional Theory, we reproduce important qualitative features of [VO(acac)[Formula: see text]] phonon modes, such as the presence of low-lying optical branches. Moreover, we evidence phonon anti-crossings involving acoustic and optical branches, yielding significant transfers of the spin-phonon coupling strength between the different modes.

Breaking the ring: 53Cr-NMR on the Cr8Cd molecular nanomagnet.

An accurate experimental characterization of finite antiferromagnetic (AF) spin chains is crucial for controlling and manipulating their magnetic properties and quantum states for potential applications in spintronics or quantum computation. In particular, finite AF chains are expected to show a different magnetic behaviour depending on their length and topology. Molecular AF rings are able to combine the quantum-magnetic behaviour of AF chains with a very remarkable tunability of their topological and geometrical properties. In this work we measure the 53Cr-NMR spectra of the Cr8Cd ring to study the local spin densities on the Cr sites. Cr8Cd can in fact be considered a model system of a finite AF open chain with an even number of spins. The NMR resonant frequencies are in good agreement with the theoretical local spin densities, by assuming a core polarization field A C = -12.7 T µ B -1. Moreover, these NMR results confirm the theoretically predicted non-collinear spin arrangement along the Cr8Cd ring, which is typical of an even-open AF spin chain.

Magnetic Exchange Interactions in the Molecular Nanomagnet Mn_{12}.

The discovery of magnetic bistability in Mn_{12} more than 20 years ago marked the birth of molecular magnetism, an extremely fertile interdisciplinary field and a powerful route to create tailored magnetic nanostructures. However, the difficulty to determine interactions in complex polycentric molecules often prevents their understanding. Mn_{12} is an outstanding example of this difficulty: although it is the forefather and most studied of all molecular nanomagnets, an unambiguous determination of even the leading magnetic exchange interactions is still lacking. Here we exploit four-dimensional inelastic neutron scattering to portray how individual spins fluctuate around the magnetic ground state, thus fixing the exchange couplings of Mn_{12} for the first time. Our results demonstrate the power of four-dimensional inelastic neutron scattering as an unrivaled tool to characterize magnetic clusters.

Portraying entanglement between molecular qubits with four-dimensional inelastic neutron scattering.

Entanglement is a crucial resource for quantum information processing and its detection and quantification is of paramount importance in many areas of current research. Weakly coupled molecular nanomagnets provide an ideal test bed for investigating entanglement between complex spin systems. However, entanglement in these systems has only been experimentally demonstrated rather indirectly by macroscopic techniques or by fitting trial model Hamiltonians to experimental data. Here we show that four-dimensional inelastic neutron scattering enables us to portray entanglement in weakly coupled molecular qubits and to quantify it. We exploit a prototype (Cr7Ni)2 supramolecular dimer as a benchmark to demonstrate the potential of this approach, which allows one to extract the concurrence in eigenstates of a dimer of molecular qubits without diagonalizing its full Hamiltonian.

Direct observation of finite size effects in chains of antiferromagnetically coupled spins.

Finite spin chains made of few magnetic ions are the ultimate-size structures that can be engineered to perform spin manipulations for quantum information devices. Their spin structure is expected to show finite size effects and its knowledge is of great importance both for fundamental physics and applications. Until now a direct and quantitative measurement of the spatial distribution of the magnetization of such small structures has not been achieved even with the most advanced microscopic techniques. Here we present measurements of the spin density distribution of a finite chain of eight spin-3/2 ions using polarized neutron diffraction. The data reveal edge effects that are a consequence of the finite size and of the parity of the chain and indicate a noncollinear spin arrangement. This is in contrast with the uniform spin distribution observed in the parent closed chain and the collinear arrangement in odd-open chains.

Magnetic properties and hyperfine interactions in Cr8, Cr7Cd, and Cr7Ni molecular rings from ¹9F-NMR.

A detailed experimental investigation of the (19)F nuclear magnetic resonance is made on single crystals of the homometallic Cr8 antiferromagnetic molecular ring and heterometallic Cr7Cd and Cr7Ni rings in the low temperature ground state. Since the F(-) ion is located midway between neighboring magnetic metal ions in the ring, the (19)F-NMR spectra yield information about the local electronic spin density and (19)F hyperfine interactions. In Cr8, where the ground state is a singlet with total spin S(T) = 0, the (19)F-NMR spectra at 1.7 K and low external magnetic field display a single narrow line, while when the magnetic field is increased towards the first level crossing field, satellite lines appear in the (19)F-NMR spectrum, indicating a progressive increase in the Boltzmann population of the first excited state S(T) = 1. In the heterometallic rings, Cr7Cd and Cr7Ni, whose ground state is magnetic with S(T) = 3/2 and S(T) = 1/2, respectively, the (19)F-NMR spectrum has a complicated structure which depends on the strength and orientation of the magnetic field, due to both isotropic and anisotropic transferred hyperfine interactions and classical dipolar interactions. From the (19)F-NMR spectra in single crystals we estimated the transferred hyperfine constants for both the F(-)-Ni(2+) and the F(-)-Cd(2+) bonds. The values of the hyperfine constants compare well to the ones known for F(-)-Ni(2+) in KNiF3 and NiF2 and for F(-)-Cr(3+) in K2NaCrF6. The results are discussed in terms of hybridization of the 2s, 2p orbitals of the F(-) ion and the d orbitals of the magnetic ion. Finally, we discuss the implications of our results for the electron-spin decoherence.

Quantum information processing with hybrid spin-photon qubit encoding.

We introduce a scheme to perform quantum information processing that is based on a hybrid spin-photon qubit encoding. The proposed qubits consist of spin ensembles coherently coupled to microwave photons in coplanar waveguide resonators. The quantum gates are performed solely by shifting the resonance frequencies of the resonators on a nanosecond time scale. An additional cavity containing a Cooper-pair box is exploited as an auxiliary degree of freedom to implement two-qubit gates. The generality of the scheme allows its potential implementation with a wide class of spin systems.

Magnetic properties and chiral states of a trimetallic uranium complex.

The magnetic properties of the triangular molecular nanomagnet [UO2L]3 (L = 2-(4-tolyl)-1,3-bis(quinolyl)malondiiminate) have been investigated through electron paramagnetic resonance spectroscopy, high-field magnetization and susceptibility measurements. The experimental findings are well reproduced by a microscopic model including exchange interactions and local crystal fields. These results show that [UO2L]3 is characterized by a non-magnetic ground doublet corresponding to two oppositely twisted chiral arrangements of the uranium moments. The non-axial character of single-ion crystal fields leads to quantum tunneling of the noncollinear magnetization in the presence of a magnetic field applied perpendicularly to the triangle plane.

Many-body models for molecular nanomagnets.

We present a flexible and effective ab initio scheme to build many-body models for molecular nanomagnets, and to calculate magnetic exchange couplings and zero-field splittings. It is based on using localized Foster-Boys orbitals as a one-electron basis. We apply this scheme to three paradigmatic systems, the antiferromagnetic rings Cr8 and Cr7Ni, and the single-molecule magnet Fe4. In all cases we identify the essential magnetic interactions and find excellent agreement with experiments.

Local spin density in the Cr7Ni antiferromagnetic molecular ring and 53Cr-NMR.

We present (53)Cr-NMR spectra collected at low temperature in a single crystal of the heterometallic antiferromagnetic (AF) ring Cr(7)Ni in the S = 1/2 ground state with the aim of establishing the distribution of the local electronic moment in the ring. Due to the poor S/N we observed only one signal which is ascribed to three almost equivalent (53)Cr nuclei in the ring. The calculated spin density in Cr(7)Ni in the ground state, with the applied magnetic field both parallel and perpendicular to the plane of the ring, turns out to be AF staggered with the greatest component of the local spin for the Cr(3+) ions next to the Ni(2+) ion. The (53)Cr-NMR frequency was found to be in good agreement with the local spin density calculated theoretically by assuming a core polarization field of H(cp) = - 11 T/µ(B) for both orientations, close to the value found previously in Cr(7)Cd. The observed orientation dependence of the local spin moments is well reproduced by the theoretical calculation and evidences the importance of single-ion and dipolar anisotropies.

Magnetic properties and relaxation dynamics of a frustrated Ni7 molecular nanomagnet.

The Ni7 nanomagnet represents an ideal model system for investigating the effects of geometrical frustration in magnetic interactions. The Ni ions in the magnetic core are arranged on two corner-sharing tetrahedra and interact through antiferromagnetic exchange couplings. We show that the high degree of frustration leads to a magnetic energy spectrum with large degeneracies which result in unusual static and dynamical magnetic properties. In particular, the relaxation dynamics of the magnetization is characterized by several distinct characteristic times. We also discuss the possible interest of Ni7 for magnetocaloric refrigeration.

Molecular nanomagnets as quantum simulators.

Quantum simulators are controllable systems that can be used to simulate other quantum systems. Here we focus on the dynamics of a chain of molecular qubits with interposed antiferromagnetic dimers. We theoretically show that its dynamics can be controlled by means of uniform magnetic pulses and used to mimic the evolution of other quantum systems, including fermionic ones. We propose two proof-of-principle experiments based on the simulation of the Ising model in a transverse field and of the quantum tunneling of the magnetization in a spin-1 system.

Linking [Fe(III)3] triangles with "double-headed"phenolic oximes.

The use of "double-headed" phenolic oximes produces a trigonal antiprismatic [Fe(III)(3)](2) cluster with an "internal cavity" filled with an additional Fe(3+) ion. Magnetic measurements reveal that the competition between different exchange interactions leads to a low-spin ground multiplet weakly separated in energy from a complex pattern of low-lying excited levels.

Relaxation dynamics of the Fe8 molecular nanomagnet as probed by nuclear magnetic resonance.

The relaxation dynamics in molecular nanomagnets can be probed by measurements of NMR 1/T(1). By modelling magnetoelastic interactions, we theoretically investigate the behaviour of the prototype Fe(8) nanomagnet. The results of our model are in agreement with AC susceptibility and recent NMR measurements.