Molecular nanomagnets as quantum simulators

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.

Proof-of-Concept Quantum Simulator Based on Molecular Spin Qudits

The use of d-level qudits instead of two-level qubits can largely increase the power of quantum logic for many applications, ranging from quantum simulations to quantum error correction. Magnetic molecules are ideal spin systems to realize these large-dimensional qudits. Indeed, their Hamiltonian can be engineered to an unparalleled extent and can yield a spectrum with many low-energy states. In particular, in the past decade, intense theoretical, experimental, and synthesis efforts have been devoted to develop quantum simulators based on molecular qubits and qudits. However, this remarkable potential is practically unexpressed, because no quantum simulation has ever been experimentally demonstrated with these systems. Here, we show the first prototype quantum simulator based on an ensemble of molecular qudits and a radiofrequency broadband spectrometer. To demonstrate the operativity of the device, we have simulated quantum tunneling of the magnetization and the transverse-field Ising model, representative of two different classes of problems. These results represent an important step toward the actual use of molecular spin qudits in quantum technologies.

Ultrafast Jahn-Teller Photoswitching in Cobalt Single-Ion Magnets

Single-ion magnets (SIMs) constitute the ultimate size limit in the quest for miniaturizing magnetic materials. Several bottlenecks currently hindering breakthroughs in quantum information and communication technologies could be alleviated by new generations of SIMs displaying multifunctionality. Here, ultrafast optical absorption spectroscopy and X-ray emission spectroscopy are employed to track the photoinduced spin-state switching of the prototypical complex [Co(terpy)2 ]2+ (terpy = 2,2':6',2″-terpyridine) in solution phase. The combined measurements and their analysis supported by density functional theory (DFT), time-dependent-DFT (TD-DFT) and multireference quantum chemistry calculations reveal that the complex undergoes a spin-state transition from a tetragonally elongated doublet state to a tetragonally compressed quartet state on the femtosecond timescale, i.e., it sustains ultrafast Jahn-Teller (JT) photoswitching between two different spin multiplicities. Adding new Co-based complexes as possible contenders in the search for JT photoswitching SIMs will greatly widen the possibilities for implementing magnetic multifunctionality and eventually controlling ultrafast magnetization with optical photons.

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.

Five-Spin Supramolecule for Simulating Quantum Decoherence of Bell States

We report a supramolecule that contains five spins of two different types and with, crucially, two different and predictable interaction energies between the spins. The supramolecule is characterized, and the interaction energies are demonstrated by electron paramagnetic resonance (EPR) spectroscopy. Based on the measured parameters, we propose experiments that would allow this designed supramolecule to be used to simulate quantum decoherence in maximally entangled Bell states that could be used in quantum teleportation.

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⟩).

Simulating Static and Dynamic Properties of Magnetic Molecules with Prototype Quantum Computers

Magnetic molecules are prototypical systems to investigate peculiar quantum mechanical phenomena. As such, simulating their static and dynamical behavior is intrinsically difficult for a classical computer, due to the exponential increase of required resources with the system size. Quantum computers solve this issue by providing an inherently quantum platform, suited to describe these magnetic systems. Here, we show that both the ground state properties and the spin dynamics of magnetic molecules can be simulated on prototype quantum computers, based on superconducting qubits. In particular, we study small-size anti-ferromagnetic spin chains and rings, which are ideal test-beds for these pioneering devices. We use the variational quantum eigensolver algorithm to determine the ground state wave-function with targeted ansatzes fulfilling the spin symmetries of the investigated models. The coherent spin dynamics are simulated by computing dynamical correlation functions, an essential ingredient to extract many experimentally accessible properties, such as the inelastic neutron cross-section.

Targeting molecular quantum memory with embedded error correction

The implementation of a quantum computer requires both to protect information from environmental noise and to implement quantum operations efficiently. Achieving this by a fully fault-tolerant platform, in which quantum gates are implemented within quantum-error corrected units, poses stringent requirements on the coherence and control of such hardware. A more feasible architecture could consist of connected memories, that support error-correction by enhancing coherence, and processing units, that ensure fast manipulations. We present here a supramolecular {Cr7Ni}-Cu system which could form the elementary unit of this platform, where the electronic spin 1/2 of {Cr7Ni} provides the processor and the naturally isolated nuclear spin 3/2 of the Cu ion is used to encode a logical unit with embedded quantum error-correction. We demonstrate by realistic simulations that microwave pulses allow us to rapidly implement gates on the processor and to swap information between the processor and the quantum memory. By combining the storage into the Cu nuclear spin with quantum error correction, information can be protected for times much longer than the processor coherence.

A trapped hexaaqua CoII complex between the polyanionic sheets of decavanadate reveals high axial anisotropy and field induced SIM behaviour

In this work, we report an inorganic compound [{Co(H₂O)₆}²⁺{Na₄V₁₀O₂₈}^2-] (1) in which the polyanionic sheets of decavanadate play the role of a diamagnetic matrix that reduces the dipolar-dipolar and spin-spin interactions between [Co(H₂O)₆]⁺² units to suppress the fast tunnelling of magnetization. Structural analysis reveals that each [Co(H₂O)₆]⁺² complex is surrounded by four decavanadates and separated by a large internuclear distance (9 Å). It was also found that the adjacent decavanadates are connected via sodium ions and form a 2D sheet of the inorganic layer in which the [Co(H₂O)₆]²⁺ ions are present in between two layers. Detailed dc (direct current) and ac (alternating current) magnetic measurements disclose the presence of large easy-axis anisotropy (D = -102 cm^-1) and field induced slow magnetic relaxation behaviour with a spin reversal barrier of U_eff = 50 K. Additionally, the temperature dependence of the relaxation time reveals that the Raman and QTM processes mainly play an important role rather than the thermally activated Orbach process in the overall relaxation dynamics of the studied compound. To analyse the electronic structure and magnetic properties of compound 1, ab initio calculations were performed which further support the experimental observations. Notably, the U_eff value of 1 represents the highest energy barrier reported for POM based SMMs with transition metal ions to date.

Probing resonating valence bond states in artificial quantum magnets

Designing and characterizing the many-body behaviors of quantum materials represents a prominent challenge for understanding strongly correlated physics and quantum information processing. We constructed artificial quantum magnets on a surface by using spin-1/2 atoms in a scanning tunneling microscope (STM). These coupled spins feature strong quantum fluctuations due to antiferromagnetic exchange interactions between neighboring atoms. To characterize the resulting collective magnetic states and their energy levels, we performed electron spin resonance on individual atoms within each quantum magnet. This gives atomic-scale access to properties of the exotic quantum many-body states, such as a finite-size realization of a resonating valence bond state. The tunable atomic-scale magnetic field from the STM tip allows us to further characterize and engineer the quantum states. These results open a new avenue to designing and exploring quantum magnets at the atomic scale for applications in spintronics and quantum simulations.

The resonating valence bond state is a spin-liquid state where spins continuously alter their singlet partners. Here Yang et al. use spin-1/2 atoms precision-placed by a scanning tunnelling microscope to create artificial quantum magnets exhibiting the resonating valence bond state.

Self-Assembly of Antiferromagnetically-Coupled Copper(II) Supramolecular Architectures with Diverse Structural Complexities

The self-assembly of 2,6-diformyl-4-methylphenol (DFMP) and 1-amino-2-propanol (AP)/2-amino-1,3-propanediol (APD) in the presence of copper(II) ions results in the formation of six new supramolecular architectures containing two versatile double Schiff base ligands (H₃L and H₅L1) with one-, two-, or three-dimensional structures involving diverse nuclearities: tetranuclear [Cu₄(HL²⁻)₂(N₃)₄]·4CH₃OH·56H₂O (1) and [Cu₄(L³⁻)₂(OH)₂(H₂O)₂] (2), dinuclear [Cu₂(H₃L1²⁻)(N₃)(H₂O)(NO₃)] (3), polynuclear {[Cu₂(H₃L1²⁻)(H₂O)(BF₄)(N₃)]·H₂O}_n (4), heptanuclear [Cu₇(H₃L1²⁻)₂(O)₂(C₆H₅CO₂)₆]·6CH₃OH·44H₂O (5), and decanuclear [Cu₁₀(H₃L1²⁻)₄(O)₂(OH)₂(C₆H₅CO₂)₄] (C₆H₅CO₂)₂·20H₂O (6). X-ray studies have revealed that the basic building block in 1, 3, and 4 is comprised of two copper centers bridged through one μ-phenolate oxygen atom from HL²⁻ or H₃L1²⁻, and one μ-1,1-azido (N₃⁻) ion and in 2, 5, and 6 by μ-phenoxide oxygen of L³⁻ or H₃L1²⁻ and μ-O²⁻ or μ₃-O²⁻ ions. H-bonding involving coordinated/uncoordinated hydroxy groups of the ligands generates fascinating supramolecular architectures with 1D-single chains (1 and 6), 2D-sheets (3), and 3D-structures (4). In 5, benzoate ions display four different coordination modes, which, in our opinion, is unprecedented and constitutes a new discovery. In 1, 3, and 5, Cu(II) ions in [Cu₂] units are antiferromagnetically coupled, with J ranging from −177 to −278 cm⁻¹.

Alignment of Axial Anisotropy in a 1D Coordination Polymer shows Improved Field Induced Single Molecule Magnet Behavior over a Mononuclear Seven Coordinated FeII Complex

Herein, we report a CN-bridged alternating Fe^II -Ni^II 1D chain to ensure the alignment of axial anisotropy and improve the single molecule magnet (SMM) behavior in seven coordinated Fe^II compound. The chain was constructed from hepta coordinated Fe(II) complex as an anisotropic building unit and diamagnetic nickel tetra cyanate as a bridging ligand. The magnetic measurements show the easy-axis anisotropy of the seven coordinated Fe(II) complex and field induced SMM behavior with spin reversal energy barrier U_eff =61(2) K (42 cm^-1 ) and pre-exponential relaxation time τ₀ =1.9×10^-8  s. The detailed analysis of the relaxation dynamics discloses that the Orbach process plays an important role in slow relaxation of magnetization for this compound. Notably, this example represents a remarkable energy barrier observed in hepta coordinated Fe(II) SMMs. The ab initio calculations estimate the magnitude of axial anisotropy and show the parallel orientation of the anisotropic axis throughout the 1D polymeric chain. In addition, it is also reported that the presence of weak π accepter ligands in the distorted axial position enhance the easy-axis anisotropy.

Remarkable Energy Barrier for Magnetization Reversal in 3D and 2D Dysprosium-Chloranilate-Based Coordination Polymers

Herein, two coordination polymers (CPs) [{Dy(Cl₂ An)_1.5 (CH₃ OH)}⋅4.5 H₂ O]_n (1) and [Dy(Cl₂ An)_1.5 (DMF)₂ ]_n (2), in which Cl₂ An is chloranilate (2,5-dihydroxy-1,4-benzoquinone dianion), exhibiting field-induced single-molecule magnet behavior with moderate barrier of magnetization reversal are reported. Detailed structural and topological analysis disclosed that 1 has a 3D network, whereas 2 has a 2D layered-type structure. In both CPs, magnetic measurements showed weak antiferromagnetic exchange interaction between the dysprosium centers and field-induced slow magnetic relaxation with barriers of 175(9)K and 145(7)K for 1 and 2, respectively. Notably, the energy barriers of magnetization reversal of 1 and 2 are remarkable for metal-chloranilate-based 3D (1) and 2D (2) CPs. The temperature and field dependence of relaxation time indicate the presence of multiple relaxation pathways, such as direct, quantum tunneling of magnetization, Raman, and Orbach processes, in both CPs. Ab initio theoretical calculations reinforced the experimentally observed higher energy barrier in 1 as compared with 2 due to the presence of large transverse anisotropy in the ground state in the latter. The average transition magnetic moment between the computed low-lying spin-orbit states also rationalized the relaxation as Orbach and Raman processes through the first excited state. BS-DFT calculations were carried out for both CPs to provide more insight into the exchange interaction.

The Second Quantum Revolution: Role and Challenges of Molecular Chemistry

Implementation of modern Quantum Technologies might benefit from the remarkable quantum properties shown by molecular spin systems. In this Perspective, we highlight the role that molecular chemistry can have in the current second quantum revolution, i.e., the use of quantum physics principles to create new quantum technologies, in this specific case by means of molecular components. Herein, we briefly review the current status of the field by identifying the key advances recently made by the molecular chemistry community, such as for example the design of molecular spin qubits with long spin coherence and the realization of multiqubit architectures for quantum gates implementation. With a critical eye to the current state-of-the-art, we also highlight the main challenges needed for the further advancement of the field toward quantum technologies development.

1D coordination polymer (OPD)2CoIISO4 showing SMM behaviour and multiple relaxation modes

A novel one-dimensional Co^II coordination polymer (OPD)₂Co^IISO₄ was formed from alternating tetrahedral sulphate anions, Co centers and molecules of 1,2-phenylenediamine (OPD). The thermal stability of the structure was confirmed up to ∼230 °C using thermogravimetry and non-ambient powder X-ray diffraction in air. The distorted pseudo-octahedral coordination sphere of Co^II ions promotes strong magnetic anisotropy. Therefore (OPD)₂Co^IISO₄ was subjected to thorough characterization with ab initio and DFT calculations along with dc magnetic measurements both of which point to strong easy-axis anisotropy (D/k_B≈-87 K, E/k_B≈ 23 K). The analysis of ac susceptibility revealed field assisted magnetic relaxation in two field regimes: a low field one with one relaxation time and a high field one where three relaxation times were distinguished. The main role in relaxations of the fastest process (τ₁) was attributed to the direct and Raman processes.

A two-qubit molecular architecture for electron-mediated nuclear quantum simulation

A molecular architecture where two vanadyl-based qubits are linked together is herein described and investigated as a platform for quantum simulation.

A switchable interaction between pairs of highly coherent qubits is a crucial ingredient for the physical realization of quantum information processing. One promising route to enable quantum logic operations involves the use of nuclear spins as protected elementary units of information, qubits. Here we propose a simple way to use fast electronic spin excitations to switch the effective interaction between nuclear spin qubits and the realization of a two-qubit molecular architecture based on highly coherent vanadyl moieties to implement quantum logic operations. Controlled generation of entanglement between qubits is possible here through chemically tuned magnetic coupling between electronic spins, which is clearly evidenced by the splitting of the vanadium(iv) hyperfine lines in the continuous-wave electron paramagnetic resonance spectrum. The system has been further characterized by pulsed electron paramagnetic resonance spectroscopy, evidencing remarkably long coherence times. The experimentally derived spin Hamiltonian parameters have been used to simulate the system dynamics under the sequence of pulses required to implement quantum gates in a realistic description that includes also the harmful effect of decoherence. This demonstrates the possibility of using this molecular complex to implement a control-Z (CZ) gate and simple quantum simulations. Indeed, we also propose a proof-of-principle experiment based on the simulation of the quantum tunneling of the magnetization in a S = 1 spin system.

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.

Investigation of easy-plane magnetic anisotropy in P-ligand square-pyramidal CoII single ion magnets

Field induced slow magnetic relaxation behavior has been studied for the first time for two P-donor ligand-based square-pyramidal Co^II complexes with an easy-plane magnetic anisotropy.

A modular design of molecular qubits to implement universal quantum gates

The physical implementation of quantum information processing relies on individual modules—qubits—and operations that modify such modules either individually or in groups—quantum gates. Two examples of gates that entangle pairs of qubits are the controlled NOT-gate (CNOT) gate, which flips the state of one qubit depending on the state of another, and the gate that brings a two-qubit product state into a superposition involving partially swapping the qubit states. Here we show that through supramolecular chemistry a single simple module, molecular {Cr₇Ni} rings, which act as the qubits, can be assembled into structures suitable for either the CNOT or gate by choice of linker, and we characterize these structures by electron spin resonance spectroscopy. We introduce two schemes for implementing such gates with these supramolecular assemblies and perform detailed simulations, based on the measured parameters including decoherence, to demonstrate how the gates would operate.

The physical implementation of quantum information processing requires individual qubits and entangling gates. Here, the authors demonstrate a modular implementation through chemistry, assembling molecular {Cr₇Ni} rings acting as qubits, with supramolecular structures realizing gates by choice of the linker.

The rise of 3-d single-ion magnets in molecular magnetism: towards materials from molecules?

Single-molecule magnets (SMMs) that contain one spin centre (so-called single-ion magnets) theoretically represent the smallest possible unit for spin-based electronic devices. The realisation of this and related technologies, depends on first being able to design systems with sufficiently large energy barriers to magnetisation reversal, Ueff, and secondly, on being able to organise these molecules into addressable arrays. In recent years, significant progress has been made towards the former goal - principally as a result of efforts which have been directed towards studying complexes based on highly anisotropic lanthanide ions, such as Tb(iii) and Dy(iii). Since 2013 however, and the remarkable report by Long and co-workers of a linear Fe(i) system exhibiting Ueff = 325 K, single-ion systems of transition metals have undergone something of a renaissance in the literature. Not only do they have important lessons to teach us about anisotropy and relaxation dynamics in the quest to enhance Ueff, the ability to create strongly coupled spin systems potentially offers access to a whole of host of 1, 2 and 3-dimensional materials with interesting structural and physical properties. This perspective summarises recent progress in this rapidly expanding sub-genre of molecular magnetism from the viewpoint of the synthetic chemist, with a particular focus on the lessons that have so far been learned from single-ion magnets of the d-block, and, the future research directions which we feel are likely to emerge in the coming years.

Making hybrid [n]-rotaxanes as supramolecular arrays of molecular electron spin qubits

Quantum information processing (QIP) would require that the individual units involved--qubits--communicate to other qubits while retaining their identity. In many ways this resembles the way supramolecular chemistry brings together individual molecules into interlocked structures, where the assembly has one identity but where the individual components are still recognizable. Here a fully modular supramolecular strategy has been to link hybrid organic-inorganic [2]- and [3]-rotaxanes into still larger [4]-, [5]- and [7]-rotaxanes. The ring components are heterometallic octanuclear [Cr7NiF8(O2C(t)Bu)16](-) coordination cages and the thread components template the formation of the ring about the organic axle, and are further functionalized to act as a ligand, which leads to large supramolecular arrays of these heterometallic rings. As the rings have been proposed as qubits for QIP, the strategy provides a possible route towards scalable molecular electron spin devices for QIP. Double electron-electron resonance experiments demonstrate inter-qubit interactions suitable for mediating two-qubit quantum logic gates.

Synthesis and reactions of N-heterocycle functionalised variants of heterometallic {Cr7Ni} rings

Here we present a series of linked cage complexes of functionalised variants of the octametallic ring {Cr₇Ni} with the general formula [ⁿPr₂NH₂][Cr₇NiF₈(O₂C^tBu)₁₅(O₂CR)], where HO₂CR is a N-heterocycle containing carboxylic acid.

A monometallic lanthanide bis(methanediide) single molecule magnet with a large energy barrier and complex spin relaxation behaviour

We report a dysprosium(iii) bis(methanediide) single molecule magnet (SMM) where stabilisation of the highly magnetic states and suppression of mixing of opposite magnetic projections is imposed by a linear arrangement of negatively-charged donor atoms supported by weak neutral donors. Treatment of [Ln(BIPMTMS)(BIPMTMSH)] [Ln = Dy, 1Dy; Y, 1Y; BIPMTMS = {C(PPh2NSiMe3)2}2-; BIPMTMSH = {HC(PPh2NSiMe3)2}-] with benzyl potassium/18-crown-6 ether (18C6) in THF afforded [Ln(BIPMTMS)2][K(18C6)(THF)2] [Ln = Dy, 2Dy; Y, 2Y]. AC magnetic measurements of 2Dy in zero DC field show temperature- and frequency-dependent SMM behaviour. Orbach relaxation dominates at high temperature, but at lower temperatures a second-order Raman process dominates. Complex 2Dy exhibits two thermally activated energy barriers (U eff) of 721 and 813 K, the largest U eff values for any monometallic dysprosium(iii) complex. Dilution experiments confirm the molecular origin of this phenomenon. Complex 2Dy has rich magnetic dynamics; field-cooled (FC)/zero-field cooled (ZFC) susceptibility measurements show a clear divergence at 16 K, meaning the magnetic observables are out-of-equilibrium below this temperature, however the maximum in ZFC, which conventionally defines the blocking temperature, T B, is found at 10 K. Magnetic hysteresis is also observed in 10% 2Dy@2Y at these temperatures. Ab initio calculations suggest the lowest three Kramers doublets of the ground 6H15/2 multiplet of 2Dy are essentially pure, well-isolated |±15/2, |±13/2 and |±11/2 states quantised along the C[double bond, length as m-dash]Dy[double bond, length as m-dash]C axis. Thermal relaxation occurs via the 4th and 5th doublets, verified experimentally for the first time, and calculated U eff values of 742 and 810 K compare very well to experimental magnetism and luminescence data. This work validates a design strategy towards realising high-temperature SMMs and produces unusual spin relaxation behaviour where the magnetic observables are out-of-equilibrium some 6 K above the formal blocking temperature.

Coherent Spin Dynamics in Molecular Cr8Zn Wheels

Controlling and understanding transitions between molecular spin states allows selection of the most suitable ones for qubit encoding. Here we present a detailed investigation of single crystals of a polynuclear Cr8Zn molecular wheel using 241 GHz electron paramagnetic resonance (EPR) spectroscopy in high magnetic field. Continuous wave spectra are well reproduced by spin Hamiltonian calculations, which evidence that transitions in correspondence to a well-defined anticrossing involve mixed states with different total spin. We studied, by means of spin echo experiments, the temperature dependence of the dephasing time (T2) down to 1.35 K. These results are reproduced by considering both hyperfine and intermolecular dipolar interactions, evidencing that the dipolar contribution is completely suppressed at the lowest temperature. Overall, these results shed light on the effects of the decoherence mechanisms, whose understanding is crucial to exploit chemically engineered molecular states as a resource for quantum information processing.

Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits

Resolving quantum many-body problems represents one of the greatest challenges in physics and physical chemistry, due to the prohibitively large computational resources that would be required by using classical computers. A solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits, i.e. by implementing a digital quantum simulator. Superconducting circuits and resonators are emerging as an extremely promising platform for quantum computation architectures, but a digital quantum simulator proposal that is straightforwardly scalable, universal, and realizable with state-of-the-art technology is presently lacking. Here we propose a viable scheme to implement a universal quantum simulator with hybrid spin-photon qubits in an array of superconducting resonators, which is intrinsically scalable and allows for local control. As representative examples we consider the transverse-field Ising model, a spin-1 Hamiltonian, and the two-dimensional Hubbard model and we numerically simulate the scheme by including the main sources of decoherence.

Heterometallic Rings: Their Physics and use as Supramolecular Building Blocks

An enormous family of heterometallic rings has been made. The first were Cr7 M rings where M = Ni(II), Zn(II), Mn(II), and rings have been made with as many as fourteen metal centers in the cyclic structure. They are bridged externally by carboxylates, and internally by fluorides or a penta-deprotonated polyol. The size of the rings is controlled through templates which have included a range of ammonium or imidazolium ions, alkali metals and coordination compounds. The rings can be functionalized to act as ligands, and incorporated into hybrid organic-inorganic rotaxanes and into molecules containing up to 200 metal centers. Physical studies reported include: magnetic measurements, inelastic neutron scattering (including single crystal measurements), electron paramagnetic resonance spectroscopy (including measurements of phase memory times), NMR spectroscopy (both solution and solid state), and polarized neutron diffraction. The rings are hence ideal for understanding magnetism in elegant exchange-coupled systems.

Electrical and thermal control of magnetic exchange interactions

We investigate the far-from-equilibrium nature of magnetic anisotropy and exchange interactions between molecular magnets embedded in a tunnel junction. By mapping to an effective spin model, these magnetic interactions can be divided into three types: isotropic Heisenberg, anisotropic Ising, and anisotropic Dzyaloshinski-Moriya contributions, which are attributed to the background nonequilibrium electronic structures. We further demonstrate that both the magnetic self- and exchange interactions can be controlled either electrically by gating and tuning the voltage bias, or thermally by adjusting the temperature bias. We show that the Heisenberg and Ising interactions scale linearly, while the Dzyaloshinski-Moriya interaction scales quadratically, with the molecule-lead coupling strength. The interactions scale linearly with the effective spin polarizations of the leads and the molecular coherence. Our results pave a way for smart control of magnetic exchange interactions at atomic and molecular levels.

Molecular nanomagnets with switchable coupling for quantum simulation

Molecular nanomagnets are attractive candidate qubits because of their wide inter- and intra-molecular tunability. Uniform magnetic pulses could be exploited to implement one- and two-qubit gates in presence of a properly engineered pattern of interactions, but the synthesis of suitable and potentially scalable supramolecular complexes has proven a very hard task. Indeed, no quantum algorithms have ever been implemented, not even a proof-of-principle two-qubit gate. Here we show that the magnetic couplings in two supramolecular {Cr7Ni}-Ni-{Cr7Ni} assemblies can be chemically engineered to fit the above requisites for conditional gates with no need of local control. Microscopic parameters are determined by a recently developed many-body ab-initio approach and used to simulate quantum gates. We find that these systems are optimal for proof-of-principle two-qubit experiments and can be exploited as building blocks of scalable architectures for quantum simulation.

Rings and threads as linkers in metal-organic frameworks and poly-rotaxanes

Coordination polymers and metal-organic rotaxane frameworks are reported where the organic linker is replaced by functionalised inorganic clusters that act as bridging ligands.

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.

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.

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.

Gd-based single-ion magnets with tunable magnetic anisotropy: molecular design of spin qubits

We report ac susceptibility and continuous wave and pulsed EPR experiments performed on GdW10 and GdW30 polyoxometalate clusters, in which a Gd3+ ion is coordinated to different polyoxometalate moieties. Despite the isotropic character of gadolinium as a free ion, these molecules show slow magnetic relaxation at very low temperatures, characteristic of single molecule magnets. For T≲200  mK, the spin-lattice relaxation becomes dominated by pure quantum tunneling events, with rates that agree quantitatively with those predicted by the Prokof'ev and Stamp model [Phys. Rev. Lett. 80, 5794 (1998)]. The sign of the magnetic anisotropy, the energy level splittings, and the tunneling rates strongly depend on the molecular structure. We argue that GdW30 molecules are also promising spin qubits with a coherence figure of merit Q(M)≳50.

Observing quantum oscillation of ground states in single molecular magnet

Single molecular magnets (SMMs) are among the potential systems for quantum memory and quantum information processing. Quantum coherence and oscillation are critical for these applications. The ground-state quantum coherence and Rabi oscillations of the SMM V15 ([V15(IV)As6(III)O42(H2O)]6-) have been studied in this context. We have affirmatively measured at 2.4 K the Rabi quantum oscillations and coherence time T2 for the ground states of the V15 ion of collective spin S=1/2, in addition to confirming the previously reported results for the S=3/2 excited states. The oscillations of S=3/2 and S=1/2 states are of different frequencies, and so can be separately selected for purposive manipulations. T2 of 188±4  ns (S=3/2) and 149±10  ns (S=1/2) are much less than T1∼12  μs and are further extendible via various approaches for qubit implementations.