A dissymmetric [Gd(2)] coordination molecular dimer hosting six addressable spin qubits

Magnetic properties and magnetocaloric effect of Ln = Dy, Tb carborane-based metal-organic frameworks

We present the synthesis and magneto-thermal properties of carborane-based lanthanide metal-organic frameworks (MOFs) with the formula {[(Ln)3(mCB-L)4(NO3)(DMF)n]·Solv}, where Ln = Dy or Tb, characterized by dc and ac susceptibility, X-ray absorption spectroscopy (XAS), X-ray magnetic circular dichroism (XMCD) and heat capacity measurements. The MOF structure is formed by polymeric 1D chains of Ln ions with three different coordination environments (Ln1, Ln2, Ln3) running along the b-axis, linked by carborane-based linkers thus to provide a 3D structure. Static magnetic measurements reveal that these MOFs behave at low temperature as a system of S* = 1/2 Ising spins, weakly interacting ferromagnetically along the 1D polymeric chain (J*/kB = +0.45 K (+0.5 K) interaction constant estimated for Dy-MOF (Tb-MOF)) and coupled to Ln ions in adjacent chains through dipolar antiferromagnetic interactions. The Dy MOF exhibits slow relaxation of magnetization through a thermally activated process, transitioning to quantum tunneling of the magnetization at low temperatures, while both compounds exhibit field-induced relaxation through a very slow, direct process. The maximum magnetic entropy changes (-ΔSmaxm) for an applied magnetic field change of 2-0 T are 5.71 J kg-1 K-1 and 4.78 J kg-1 K-1, for Dy and Tb MOFs, respectively, while the magnetocaloric effect (MCE) peak for both occurs at T ∼ 1.6 K, approximately double that for the Gd counterpart.

Endohedral metallofullerene molecular nanomagnets

Magnetic lanthanide (Ln) metal complexes exhibiting magnetic bistability can behave as molecular nanomagnets, also known as single-molecule magnets (SMMs), suitable for storing magnetic information at the molecular level, thus attracting extensive interest in the quest for high-density information storage and quantum information technologies. Upon encapsulating Ln ion(s) into fullerene cages, endohedral metallofullerenes (EMFs) have been proven as a promising and versatile platform to realize chemically robust SMMs, in which the magnetic properties are able to be readily tailored by altering the configurations of the encapsulated species and the host cages. In this review, we present critical discussions on the molecular structures and magnetic characterizations of EMF-SMMs, with the focus on their peculiar molecular and electronic structures and on the intriguing molecular magnetism arising from such structural uniqueness. In this context, different families of magnetic EMFs are summarized, including mononuclear EMF-SMMs wherein single-ion anisotropy is decisive, dinuclear clusterfullerenes whose magnetism is governed by intramolecular magnetic interaction, and radical-bridged dimetallic EMFs with high-spin ground states that arise from the strong ferromagnetic coupling. We then discuss how molecular assemblies of SMMs can be constructed, in a way that the original SMM behavior is either retained or altered in a controlled manner, thanks to the chemical robustness of EMFs. Finally, on the basis of understanding the structure-magnetic property correlation, we propose design strategies for high-performance EMF-SMMs by engineering ligand fields, electronic structures, magnetic interactions, and molecular vibrations that can couple to the spin states.

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.

Spin Qubit in a 2D GdIII NaI -Based Oxamato Supramolecular Coordination Framework

Qubits are the basic unit of quantum information and computation. To realize quantum computing and information processing, the decoherence times of qubits must be long enough. Among the studies of molecule-based electron spin qubits, most of the work focused on the ions with the spin S=1/2, where only single-bit gates can be constructed. However, quantum operations require the qubits to interact with each other, so people gradually carry out relevant research in ions or systems with S>1/2 and multilevel states. In this work, a two-dimensional (2D) oxygen-coordinated GdIII NaI -based oxamato supramolecular coordination framework, Na[Gd(4-HOpa)4 (H2 O)] ⋅ 2H2 O (1, 4-HOpa=N-4-hydroxyphenyloxamate), was selected as a possible carrier of qubit. The field-induced slow magnetic relaxation shows this system has phonon bottleneck (PB) effect at low temperatures with a very weak magnetic anisotropy. The pulse electron paramagnetic resonance studies show the spin-lattice and spin-spin relaxation times are T1 =1.66 ms at 4 K and Tm =4.25 μs at 8 K for its diamagnetically diluted sample (1Gd0.12 %). It suggested that the relatively long decoherence time is mainly ascribed to its near isotropic and the PB effect from resonance phonon trapped for pure sample, while the dilution further improves its qubit performance.

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.

Electron Paramagnetic Resonance Spectra of Pentagonal Bipyramidal Gadolinium Complexes

Gadolinium is a special case in spectroscopy because of the near isotropic nature of the 4f⁷ configuration of the +3 oxidation state. Gd³⁺ complexes have been studied in several symmetries to understand the underlying mechanisms of the ground state splitting. The abundance of information in Gd³⁺ spectra can be used as a probe for properties of the other rare earth ions in the same complexes. In this work, the zero-field splitting (ZFS) of a series of Gd³⁺ pentagonal bipyramidal complexes of the form [GdX₁X₂(L_eq)₅]ⁿ⁺ [n = 1, X = axial ligands: Cl^-, ^-O^tBu, ^-OArF₅ or n = 3, X = ^tBuPO(NHⁱPr)₂, L_eq = equatorial ligand: Py, THF or H₂O] with near fivefold symmetry axes along X¹-Gd-X² was investigated. The ZFS parameters were determined by fitting of room-temperature continuous wave electron paramagnetic resonance (EPR) spectra (at X-, K-, and Q-band) to a spin Hamiltonian incorporating extended Stevens operators compatible with C₅ symmetry. Examination of the acquired parameters led to the conclusion that the ZFS is dominated by the B₂⁰ term and that the magnitude of B₂⁰ is almost entirely dependent on, and inversely proportional to, the donor strength of the axial ligands. Surveying the continuous shape measure and the X¹-Gd-X² angle of the complexes showed that there is some correlation between the proximity of each complex to D_5h symmetry and the magnitude of the B₆⁵ parameter, but that the deformation of the X¹-Gd-X² angle is more significant than other distortions. Finally, the magnitude of B₂⁰ was found to be inversely proportional to the thermal barrier for the reversal of the magnetic moment (U_eff) of the corresponding isostructural Dy³⁺ complexes.

Fe-Gd Ferromagnetic Cyclic Coordination Cluster [FeIII4GdIII4(teaH)8(N3)8(H2O)] with Magnetic Anisotropy─Theory and Experiment

The synthesis, structural, and magnetic characterization of [Fe^III₄Ln^III₄(teaH)₈(N₃)₈(H₂O)] (Ln = Gd and Y) and the previously reported isostructural Dy analogue are discussed. The commonly held belief that both Fe^III and Gd^III can be regarded as isotropic ions is shown to be an oversimplification. This conclusion is derived from the magnetic data for the Y^III analogue in terms of the zero-field splitting seen for Fe^III and from the fact that the magnetic data for the new Gd^III analogue can only be fit employing an additional anisotropy term for the Gd^III ions. Furthermore, the Fe₄Gd₄ ring shows slow relaxation of magnetization. Our analysis of the experimental magnetic data employs both density functional theory as well as the finite-temperature Lanczos method which finally enables us to provide an almost perfect fit of magnetocaloric properties.

Modular Approach to Creating Functionalized Surface Arrays of Molecular Qubits

The quest for developing quantum technologies is driven by the promise of exponentially faster computations, ultrahigh performance sensing, and achieving thorough understanding of many-particle quantum systems. Molecular spins are excellent qubit candidates because they feature long coherence times, are widely tunable through chemical synthesis, and can be interfaced with other quantum platforms such as superconducting qubits. A present challenge for molecular spin qubits is their integration in quantum devices, which requires arranging them in thin films or monolayers on surfaces. However, clear proof of the survival of quantum properties of molecular qubits on surfaces has not been reported so far. Furthermore, little is known about the change in spin dynamics of molecular qubits going from the bulk to monolayers. Here, a versatile bottom-up method is reported to arrange molecular qubits as functional groups of self-assembled monolayers (SAMs) on surfaces, combining molecular self-organization and click chemistry. Coherence times of up to 13 µs demonstrate that qubit properties are maintained or even enhanced in the monolayer.

Evidence of symmetry breaking in a Gd2 di-nuclear molecular polymer

A chiral 3D coordination compound, [Gd₂(L)₂(ox)₂(H₂O)₂], arranged around a dinuclear Gd unit has been characterized by X-ray photoemission and X-ray absorption measurements in the context of density functional theory studies. Core level photoemission of the Gd 5p multiplet splittings indicates that spin orbit coupling dominates over j-J coupling evident in the 5p core level spectra of Gd metal. Indications of spin-orbit coupling are consistent with the absence of inversion symmetry due to the ligand field. Density functional theory predicts antiferromagnet alignment of the Gd₂ dimers and a band gap of the compound consistent with optical absorption.

Unparalleled selectivity and electronic structure of heterometallic [LnLn'Ln] molecules as 3-qubit quantum gates

Heterometallic lanthanide [LnLn'] coordination complexes that are accessible thermodynamically are very scarce because the metals of this series have very similar chemical behaviour. Trinuclear systems of this category have not been reported. A coordination chemistry scaffold has been shown to produce molecules of type [LnLn'Ln] of high purity, i.e. exhibiting high metal distribution ability, based on their differences in ionic radius. Through a detailed analysis of density functional theory (DFT) based calculations, we discern the energy contributions that lead to the unparalleled chemical selectivity of this molecular system. Some of the previously reported examples are compared here with the newly prepared member of this exotic list, [Er₂Pr(LA)₂(LB)₂(py)(H₂O)₂](NO₃) (1) (H₂LA and H₂LB are two β-diketone ligands). A magnetic analysis extracted from magnetization and calorimetry determinations identifies the necessary attributes for it to act as an addressable, conditional multiqubit spin-based quantum gate. Complementary ab initio calculations confirm the feasibility of these complexes as composite quantum gates, since they present well-isolated ground states with highly anisotropic and distinct g-tensors. The electronic structure of 1 has also been analyzed by EPR. Pulsed experiments have allowed the establishment of the quantum coherence of the transitions within the relevant spin states, as well as the feasibility of a coherent control of these states via nutation experiments.

Trinuclear Cobalt(II) Triple Helicate with a Multidentate Bithiazolebis(oxamate) Ligand as a Supramolecular Nanomagnet

The cobalt(II)-mediated self-assembly of the potentially tris(chelating) N,N'-2,2'-(4,4'-bithiazole)bis(oxamate) (dabtzox) ligand gives a new metal-organic supramolecular nanomagnet of formula K₆Co₃(dabtzox)₃·8H₂O·MeOH (1) featuring a unique linear triple-stranded trinuclear structure of the helicate type.

Laser-Controlled Implementation of Controlled-NOT, Hadamard, SWAP, and Pauli Gates as Well as Generation of Bell States in a 3d-4f Molecular Magnet

Using high-level ab initio many-body theory, we theoretically propose that the Dy and the Ni atoms in the [Dy₂Ni₂(L)₄(NO₃)₂(DMF)₂] real molecular magnet as well as in its core, that is, the [Dy₂Ni₂O₆] system, act as two-level qubit systems. Despite their spatial proximity we can individually control each qubit in this highly correlated real magnetic system through specially designed laser-pulse combinations. This allows us to prepare any desired two-qubit state and to build several classical and quantum logic gates, such as the two-qubit (binary) CNOT gate with three distinct laser pulses. Other quantum logic gates include the single-qubit (unary) quantum X, Y, and Z Pauli gates; the Hadamard gate (which necessitates the coherent quantum superposition of two many-body electronic states); and the SWAP gate (which plays an important role in Shor's algorithm for integer factorization). Finally, by sequentially using the achieved CNOT and Hadamard gates we are able to obtain the maximally entangled Bell states, for example, (12)(|00⟩ + |11⟩).

Designed polynuclear lanthanide complexes for quantum information processing

The design of dissymmetric organic ligands featuring combinations of 1,3-diketone and 2,6-diacetylpyridine coordination pockets has been exploited to produce dinuclear and trinuclear lanthanide-based coordination compounds. These molecules exhibit two or more non-equivalent Ln ions, most remarkably enabling the access to well-defined heterolanthanide compositions. The site-selective disposition of each metal ion within the molecular entities allows the study of each centre individually as a spin-based quantum bit, affording unparalleled versatility for quantum gate design. The inherent weak interaction between the Ln ions permits the performance of multi-qubit quantum logical operations realized through their derived magnetic states, or implementing quantum-error correction protocols. The different studies performed to date on these systems are revised, showing their vast potential within spin-based quantum information processing.

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.

Accessing Lanthanide-to-Lanthanide Energy Transfer in a Family of Site-Resolved [LnIII LnIII '] Heterodimetallic Complexes

The ligand H₃ L (6-[3-oxo-3-(2-hydroxyphenyl)propionyl]pyridine-2-carboxylic acid), which exhibits two different coordination pockets, has been exploited to engender and study energy transfer (ET) in two dinuclear [Ln^III Ln^III '] analogues of interest, [EuYb] and [NdYb]. Their structural and physical properties have been compared with newly synthesised analogues featuring no possible ET ([EuLu], [NdLu], and [GdYb]) and with the corresponding homometallic [EuEu] and [NdNd] analogues, which have been previously reported. Photophysical data suggest that ET between Eu^III and Yb^III does not occur to a significant extent, whereas emission from Yb^III originates from sensitisation of the ligand. In contrast, energy migration seems to be occurring between the two Nd^III centres in [NdNd], as well as in [NdYb], in which Yb^III luminescence is thus, in part, sensitised by ET from Nd. This study shows the versatility of this molecular platform to further the investigation of lanthanide-to-lanthanide ET phenomena in defined molecular systems.

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

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.

Chemical tuning of spin clock transitions in molecular monomers based on nuclear spin-free Ni(ii)

We report the existence of a sizeable quantum tunnelling splitting between the two lowest electronic spin levels of mononuclear Ni complexes. The level anti-crossing, or magnetic "clock transition", associated with this gap has been directly monitored by heat capacity experiments. The comparison of these results with those obtained for a Co derivative, for which tunnelling is forbidden by symmetry, shows that the clock transition leads to an effective suppression of intermolecular spin-spin interactions. In addition, we show that the quantum tunnelling splitting admits a chemical tuning via the modification of the ligand shell that determines the crystal field and the magnetic anisotropy. These properties are crucial to realize model spin qubits that combine the necessary resilience against decoherence, a proper interfacing with other qubits and with the control circuitry and the ability to initialize them by cooling.