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.

Effect of a small loss or gain in the periodic nonlinear Schrödinger anomalous wave dynamics.

The focusing nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability of quasimonochromatic waves in weakly nonlinear media, the main physical mechanism for the appearance of anomalous (rogue) waves (AWs) in nature. In this paper, concentrating on the simplest case of a single unstable mode, we study the special Cauchy problem for the NLS equation perturbed by a linear loss or gain term, corresponding to periodic initial perturbations of the unstable background solution of the NLS. Using the finite gap method and the theory of perturbations of soliton partial differential equations, we construct the proper analytic model describing quantitatively how the solution evolves after a suitable transient into slowly varying lower dimensional patterns (attractors) on the (x,t) plane, characterized by ΔX=L/2 in the case of loss and by ΔX=0 in the case of gain, where ΔX is the x shift of the position of the AW during the recurrence, and L is the period. This process is described, to leading order, in terms of elementary functions of the initial data. Since dissipation can hardly be avoided in all natural phenomena involving AWs, and since a small dissipation induces O(1) effects on the periodic AW dynamics, generating the slowly varying loss or gain attractors analytically described in this paper, we expect that these attractors together with their generalizations corresponding to more unstable modes will play a basic role in the theory of periodic AWs in nature.

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.

Fermi-Pasta-Ulam-Tsingou recurrence of periodic anomalous waves in the complex Ginzburg-Landau and in the Lugiato-Lefever equations.

The complex Ginzburg-Landau (CGL) equation, an envelope model relevant in the description of several natural phenomena like binary-fluid convection and second-order phase transitions, and the Lugiato-Lefever (LL) equation, describing the dynamics of optical fields in pumped lossy cavities, can be viewed as nonintegrable generalizations of the nonlinear Schrödinger (NLS) equation, including diffusion, linear and nonlinear loss or gain terms, and external forcing. In this paper we treat the nonintegrable terms of both equations as small perturbations of the integrable focusing NLS equation, and we study the Cauchy problem of the CGL and LL equations corresponding to periodic initial perturbations of the unstable NLS background solution, in the simplest case of a single unstable mode. Using the approach developed in a recent paper by the authors with P. G. Grinevich [Phys. Rev. E 101, 032204 (2020)10.1103/PhysRevE.101.032204], based on the finite gap method and the theory of perturbations of soliton PDEs, we construct the proper analytic models describing quantitatively how the solution evolves, after a suitable transient, into a Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence of anomalous waves (AWs) described by slowly varying lower dimensional patterns (attractors) in the (x,t) plane, characterized by Δx=L/2 or Δx=0 in the case in which loss or gain, respectively, effects prevail, where Δx is the x-shift of the position of the AW during the recurrence and L is the period. We also obtain, in the CGL case, the analytic condition for which loss and gain exactly balance, stabilizing the ideal FPUT recurrence of periodic NLS AWs; such a stabilization is not possible in the LL case due to the external forcing. These processes are described, to leading order, in terms of elementary functions of the initial data in the CGL case, and in terms of elementary and special functions of the initial data in the LL case.

Use of low-dose radioiodine ablation for Graves' orbitopathy: results of a pilot, perspective study in a small series of patients.

OBJECTIVE: Elimination of thyroid antigens by total thyroid ablation (TTA), namely, thyroidectomy followed by radioiodine, may be beneficial for Graves' Orbitopathy (GO). TTA is usually performed with a 131I dose of 30 mCi. In Italy, this dose must be followed by a 24-h protected hospitalization, with increase in the waiting lists. In contrast, a 15 mCi dose can be given without hospitalization and with lower costs. Here, we investigated whether a lower dose of radioiodine can be used to ablate thyroid remnants in patients with GO, after thyroidectomy. METHODS: The study was performed in two small groups of consecutive thyroidectomized patients (six patients per group) with Graves' hyperthyroidism and GO. Patients underwent ablation with either 15 or 30 mCi of 131I following treatment with recombinant human TSH (rhTSH). The primary outcome was rhTSH-stimulated serum thyroglobulin (Tg) at 6 months. The secondary outcome was baseline Tg at 6 months. RESULTS: Baseline Tg and rhTSH-stimulated Tg after at 6 months did not differ between two groups, suggesting a similar extent of ablation. rhTSH-stimulated Tg was reduced significantly compared with rhTSH-stimulated Tg at ablation in both groups. GO outcome following treatment with intravenous glucocorticoids did not differ between the two groups. CONCLUSIONS: Our findings may provide a preliminary basis for the use of a 15 mCi dose of radioiodine upon rhTSH stimulation in thyroidectomized patients with Graves' hyperthyroidism and GO.

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.

Thyroglobulin autoantibodies switch to immunoglobulin (Ig)G1 and IgG3 subclasses and preserve their restricted epitope pattern after 131I treatment for Graves' hyperthyroidism: the activity of autoimmune disease influences subclass distribution but not epitope pattern of autoantibodies.

The subclass distribution of thyroglobulin autoantibodies (TgAb) is debated, whereas their epitope pattern is restricted. Radioidine ((131)I) treatment for Graves' disease (GD) induces a rise in TgAb levels, but it is unknown whether it modifies subclass distribution and epitope pattern of TgAb as well. We collected sera from GD patients before (131) I treatment and 3 and 6 months thereafter. We measured total TgAb, TgAb light chains and TgAb subclasses by enzyme-linked immunosorbent assay (ELISA) in 25 patients. We characterized the TgAb epitope pattern in 30 patients by inhibiting their binding to (125-) (I) Tg by a pool of four TgAb-Fab (recognizing Tg epitope regions A, B, C and D) and to Tg in ELISA by each TgAb-Fab. Total TgAb immunoglobulin (Ig)G rose significantly (P = 0.024). TgAb κ chains did not change (P = 0.052), whereas TgAb λ chains increased significantly (P = 0.001) and persistently. We observed a significant rise in IgG1 and IgG3 levels after (131)I (P = 0.008 and P = 0.006, respectively), while IgG2 and IgG4 levels did not change. The rise of IgG1 was persistent, that of IgG3 transient. The levels of inhibition of TgAb binding to Tg by the TgAb-Fab pool were comparable. A slight, non-significant reduction of the inhibition by the immune-dominant TgAb-Fab A was observed 3 and 6 months after (131)I. We conclude that (131)I treatment for GD increases the levels of the complement-activating IgG1 and IgG3 subclasses and does not influence significantly the epitope pattern of TgAb. In autoimmune thyroid disease subclass distribution of autoantibodies is dynamic in spite of a stable epitope pattern.

Detection of metastases from differentiated thyroid cancer by different imaging techniques (neck ultrasound, computed tomography and [18F]-FDG positron emission tomography) in patients with negative post-therapeutic ¹³¹I whole-body scan and detectable serum thyroglobulin levels.

INTRODUCTION: DTC patients having detectable Tg and negative post-therapeutic (131)I-WBS have to be investigated by different imaging techniques to detect metastases. PURPOSE: Comparison of neck US, CT and [18F]-FDG PET scan. METHODS: In 49 DTC patients with biochemical disease, neck was examined by US, CT and [18F]-FDG PET. FNA was performed and Tg was determined by FNA-Tg in selected cases of suspicious lymph nodes. Thorax was examined by CT and PET. Serum Tg was measured on LT4 therapy (basal Tg) and after the stimulation with recombinant human TSH (peak Tg). RESULTS: A thyroid remnant was seen by US, CT and PET in eight patients; recurrences were seen by US, CT and PET in six, five and five patients, respectively. Two metastatic nodes were identified by US and CT but not by PET. Lung micronodules were detected by CT in 7/49 (14.3 %) patients and by FDG PET in three of them. Basal Tg ranged from 0.5-1,725 ng/ml while peak Tg ranged from 0.5 to 2,135 ng/ml: the distribution between positive and negative patients was similar. Bone scan was negative in all cases. CONCLUSIONS: In DTC patients with detectable Tg and negative I-131 post-therapy WBS, imaging examination revealed remnant or metastases in 43 % of cases. Remnant and recurrences were equally detected by the three techniques; US was better than [18F]-FDG PET for lymph node metastases since this latter method can give false both positive and negative results; chest examination is best made by CT versus FDG PET due to its higher spatial resolution.

Whispering gallery mode diamond resonator.

We demonstrate a nearly spherical diamond whispering gallery mode resonator with quality factor (Q factor) Q=2.4×10(7) limited by material loss approaching α=4×10(-3) cm(-1). The Q factor does not depend on the wavelength: it is approximately the same at 1319 and 1550 nm. Resonators with this range of Q (<10 MHz at 1550 nm wavelength) are attractive for laser locking and stabilization. Applications such as stable compact optical comb generators as well as Raman optical frequency shifters will be feasible with further improvement of the material.

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.

Salivary glands ultrasound examination after radioiodine-131 treatment for differentiated thyroid cancer.

BACKGROUND: The most important side effect of radioiodine ((131)I) therapy is sialoadenitis and xerostomy. AIM: To evaluate by ultrasound (US) parotid and submandibular glands after (131)I therapy for differentiated thyroid cancer (DTC). PATIENTS: Seventy-six subjects thyroidectomized for DTC submitted to salivary glands US examination. Forty-three of them had been previously treated with (131)I: 22 with 1.11 GBq (30 mCi) for remnant ablation, and 21 with higher doses [up to 44.4 GBq (1200 mCi)] for metastases. Thirty-three subjects studied before (131)I therapy served as controls. Parotid and submandibular volume, homogeneity, and echogenicity were determined. (131)I-treated patients filled a questionnaire about sialoadenitis symptoms. RESULTS: Parotid gland volume was significantly higher in treated patients (28.3±16.2 ml) than in untreated patients (20.7±10.4 ml, p=0.0154) and related to the time from last (131)I therapy. Three had parotid volume <1.5 ml and complained severe xerostomy. Submandibular gland volume was similar in treated (11.2±7.6 ml) and untreated patients (8.6±4.2 ml, p=0.0602). Homogeneity and echogenicity were similar in treated and untreated patients. Sialoadenitis symptoms were reported in 26% and were related to the (131)I cumulative dose. Symptoms were not related to gland volume. Hypoechogenicity and inhomogeneity of the parotids were more frequent in patients with salivary stickiness. CONCLUSION: Parotid, but not submandibular, volume is increased after (131)I treatment depending on the received activity and the time from irradiation but not on sialoadenitis symptoms. Xerostomy is associated to gland atrophy at US.