A modular design of molecular qubits to implement universal quantum gates

Weak Exchange Interactions in Multispin Systems: EPR Studies of Metalloporphyrins Decorated with {Cr7Ni} Rings

Both metalloporphyrins and heterometallic {Cr7Ni} rings are of significant research interest due to their proposed roles in quantum information processing devices. In this study, we present a series of complexes in which [Cr7NiF3(Etglu)(O2CtBu)15] (N-EtgluH5 = N-ethyl-d-glucamine) heterometallic rings are coordinated to metalloporphyrin linkers: the symmetric [M(TPyP)] for M = Cu2+, VO2+, and H2TPyP = 5,10,15,20-tetra(4-pyridyl)porphyrin; and the asymmetric [{VO}(TrPPyP)] for H2(TrPPyP) = 5,10,15-(triphenyl)-20-(4-pyridyl)porphyrin. The magnetic interactions present in these complexes are unraveled using the continuous wave (CW) electron paramagnetic resonance (EPR) technique. The nature of the coupling between the {Cr7Ni} rings and the central metalloporphyrin is assessed by numerical simulations of CW EPR spectra and determined to be on the order of 0.01 cm-1, larger than the dipolar ones and suitable for individual spin addressability in multiqubit architectures.

Ligand Effects on the Spin Relaxation Dynamics and Coherent Manipulation of Organometallic La(II) Potential Qudits

We present pulsed electron paramagnetic resonance (EPR) studies on three La(II) complexes, [K(2.2.2-cryptand)][La(Cp')3] (1), [K(2.2.2-cryptand)][La(Cp″)3] (2), and [K(2.2.2-cryptand)][La(Cptt)3] (3), which feature cyclopentadienyl derivatives as ligands [Cp' = C5H4SiMe3; Cp″ = C5H3(SiMe3)2; Cptt = C5H3(CMe3)2] and display a C3 symmetry. Long spin-lattice relaxation (T1) and phase memory (Tm) times are observed for all three compounds, but with significant variation in T1 among 1-3, with 3 being the slowest relaxing due to higher s-character of the SOMO. The dephasing times can be extended by more than an order of magnitude via dynamical decoupling experiments using a Carr-Purcell-Meiboom-Gill (CPMG) sequence, reaching 161 μs (5 K) for 3. Coherent spin manipulation is performed by the observation of Rabi quantum oscillations up to 80 K in this nuclear spin-rich environment (1H, 13C, and 29Si). The high nuclear spin of 139La (I = 7/2), and the ability to coherently manipulate all eight hyperfine transitions, makes these molecules promising candidates for application as qudits (multilevel quantum systems featuring d quantum states; d >2) for performing quantum operations within a single molecule. Application of HYSCORE techniques allows us to quantify the electron spin density at ligand nuclei and interrogate the role of functional groups to the electron spin relaxation properties.

Optical Phenomena in Molecule-Based Magnetic Materials

Since the last century, we have witnessed the development of molecular magnetism which deals with magnetic materials based on molecular species, i.e., organic radicals and metal complexes. Among them, the broadest attention was devoted to molecule-based ferro-/ferrimagnets, spin transition materials, including those exploring electron transfer, molecular nanomagnets, such as single-molecule magnets (SMMs), molecular qubits, and stimuli-responsive magnetic materials. Their physical properties open the application horizons in sensors, data storage, spintronics, and quantum computation. It was found that various optical phenomena, such as thermochromism, photoswitching of magnetic and optical characteristics, luminescence, nonlinear optical and chiroptical effects, as well as optical responsivity to external stimuli, can be implemented into molecule-based magnetic materials. Moreover, the fruitful interactions of these optical effects with magnetism in molecule-based materials can provide new physical cross-effects and multifunctionality, enriching the applications in optical, electronic, and magnetic devices. This Review aims to show the scope of optical phenomena generated in molecule-based magnetic materials, including the recent advances in such areas as high-temperature photomagnetism, optical thermometry utilizing SMMs, optical addressability of molecular qubits, magneto-chiral dichroism, and opto-magneto-electric multifunctionality. These findings are discussed in the context of the types of optical phenomena accessible for various classes of molecule-based magnetic materials.

Challenges for exploiting nanomagnet properties on surfaces

Molecular complexes with single-molecule magnet (SMM) or qubit properties, commonly called molecular nanomagnets, are great candidates for information storage or quantum information processing technologies. However, the implementation of molecular nanomagnets in devices for the above-mentioned applications requires controlled surface deposition and addressing the nanomagnets' properties on the surface. This Perspectives paper gives a brief overview of molecular properties on a surface relevant for magnetic molecules and how they are affected when the molecules interact with a surface; then, we focus on systems of increasing complexity, where the relevant SMMs and qubit properties have been observed for the molecules deposited on surfaces; finally, future perspectives, including possible ways of overcoming the problems encountered so far are discussed.

Spin qubits of Cu(II) doped in Zn(II) metal-organic frameworks above microsecond phase memory time

With the aim of creating Cu(II) spin qubits in a rigid metal-organic framework (MOF), this work demonstrates a doping of 5 %, 2 %, 1 %, and 0.1 % mol of Cu(II) ions into a perovskite-type MOF [CH6 N3 ][ZnII (HCOO)3 ]. The presence of dopant Cu(II) sites are confirmed with anisotropic g-factors (gx =2.07, gy =2.12, and gz =2.44) in the S=1/2 system by experimentally and theoretically. Magnetic dynamics indicate the occurrence of a slow magnetic relaxation via the direct and Raman processes under an applied field, with a relaxation time (τ) of 3.5 ms (5 % Cu), 9.2 ms (2 % Cu), and 15 ms (1 % Cu) at 1.8 K. Furthermore, pulse-ESR spectroscopy reveals spin qubit properties with a spin-spin relaxation (phase memory) time (T2 ) of 0.21 μs (2 %Cu), 0.39 μs (1 %Cu), and 3.0 μs (0.1 %Cu) at 10 K as well as Rabi oscillation between MS =±1/2 spin sublevels. T2 above microsecond is achieved for the first time in the Cu(II)-doped MOFs. It can be observed at submicrosecond around 50 K. These spin relaxations are very sensitive to the magnetic dipole interactions relating with cross-relaxation between the Cu(II) sites and can be tuned by adjusting the dopant concentration.

Molecular nanomagnets: a viable path toward quantum information processing?

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

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

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

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.

Triggering single-molecule qubit spin dynamics via non-Abelian geometric phase effects

We illustrate how macroscopic rotations can be utilised to trigger and control a spin dynamics within the ground doublet of both Kramers and non-Kramers-type molecular nanomagnets via the non-Abelian character of the time-evolution operator. For Kramers magnets, we show how this effect can be harnessed to realise single-qubit quantum gates and give the explicit example of a recently reported CoCl2(tu)4 single-molecule magnet (SMM). We demonstrate that gating operations could be performed on this magnet in as fast as 10 ps before the breakdown of adiabaticity, much faster than typical spin-lattice relaxation times. Based on this effect, we also suggest CoCl2(tu)4 as a quantum gyroscope for sensing yaw-axis rotations. For integer spin nanomagnets where non-axial crystal field interactions often lift ground state degeneracy, we show how spin dynamics from the non-Abelian geometric propagator can be recovered using non-adiabatic macroscopic rotations not-necessarily resonant with the tunnel splitting gap. Using the well-known TbPc2 single-ion magnet as a further example, we identify an experimentally plausible non-adiabatic rotation that induces a coherent superposition of tunnelling ground states, tantamount to preparing each member of a TbPc2 ensemble in the maximal angular momentum state |mJ = 6〉. The detection of an ensuing coherent oscillation of the macroscopic magnetisation polarised along the TbPc2 principal magnetic axis after the completed rotation could then proceed via time-resolved magnetisation measurements.

PDI-trityl dyads as photogenerated molecular spin qubit candidates

Owing to their potential applications in the field of quantum information science, photogenerated organic triplet-radical conjugates have attracted an increasing amount of attention recently. Typically, these compounds are composed of a chromophore appended to a stable radical. After initialisation of the system by photoexcitation, a highly spin-polarised quartet state may be generated, which serves as a molecular spin qubit candidate. Here, we investigate three perylene diimide (PDI)-based chromophore-radical systems with different phenylene linkers and radical counterparts by both optical spectroscopy and transient electron paramagnetic resonance (EPR) techniques. Femtosecond transient absorption measurements demonstrate chromophore triplet state formation on a picosecond time scale for PDI-trityl dyads, while excited state deactivation is found to be slowed down considerably in a PDI-nitroxide analogue. The subsequent investigation of the coherent spin properties by transient EPR confirms quartet state formation by triplet-doublet spin mixing for all investigated dyads and the suitability of the two studied PDI-trityl dyads as spin qubit candidates. In particular, we show that using tetrathiaryl trityl as the radical counterpart, an intense spin polarisation is observed even at room temperature and quartet state coherence times of 3.0 μs can be achieved at 80 K, which represents a considerable improvement compared to previously studied systems.

Room Temperature Electron Spin Coherence in Photogenerated Molecular Spin Qubit Candidates

One of the main challenges in the emerging field of molecular spintronics is the identification of new spin qubit materials for quantum information applications. In this regard, recent work has shown that photoexcited chromophore-radical systems are promising candidates to expand our repertoire of suitable candidate molecules. Here, we investigate a series of three chromophore-radical compounds composed of a perylene diimide (PDI) chromophore and a stable 2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPO) radical by transient electron paramagnetic resonance (EPR) techniques. We explore the influence of isotope labeling of the TEMPO moiety on the EPR spectra and electron spin coherence times of the molecular quartet states generated upon photoexcitation and illustrate that (i) a coherent manipulation of the spin state is possible in these systems even at room temperature and that (ii) a spin coherence time of 0.7 μs can be achieved under these conditions. This demonstration of electron spin coherence at ambient temperatures paves the way for practical applications of such systems in functional molecular devices.

VdW Mediated Strong Magnetic Exchange Interactions in Chains of Hydrogen-Free Sublimable Molecular Qubits

Sulfur-rich molecular complexes of dithiolene-like ligands are appealing candidates as molecular spin qubits because spin coherence properties are enhanced in hydrogen-free environments. Herein, we employ the hydrogen-free mononegative 1,3,2-dithiazole-4-thione-5-thiolate (dttt^-) ligand as an alternative to common dinegative dithiolate ligands. We report the first synthesis and structural characterization of its Cu²⁺, Ni²⁺, and Pt²⁺ neutral complexes. The XPS analysis of thermal deposition of [Cu(dttt)₂] in UHV conditions indicates that films of intact molecules can be deposited on surfaces by sublimation. Thanks to a combined approach employing DC magnetometry and DFT calculations, we highlighted AF exchange interactions of 108 cm^-1 and 36 cm^-1 attributed to the two different polymorph phases. These couplings are exclusively mediated by S···S VdW interactions, which are facilitated by the absence of counterions and made particularly efficient by the diffuse electron density on S atoms. Furthermore, the spin dynamics of solid-state magnetically diluted samples was investigated. The longest observed T _m is 2.3 μs at 30 K, which significantly diverges from the predicted T _m > 100 μs. These results point to the diluting matrix severely affecting the coherence lifetime of Cu²⁺ species via different factors, such as the contributions of neighboring ¹⁴N nuclei and the formation of radical impurities in a non-completely controllable way. However, the ease of processing [Cu(dttt)₂] via thermal sublimation can allow dispersion in matrices better suited for coherent spin manipulation of isolated molecules and the realization of AF-coupled VdW structures on surfaces.

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.

Observation of slow magnetic relaxation phenomena in spatially isolated π-radical ions

The use of molecular spins as quantum bits is fascinating because it offers a wide range of strategies through chemical modifications. In this regard, it is very interesting to search for organic radical ions that have small spin-orbit coupling values. On the other hand, the feature of the magnetic relaxation of π-organic radical ions is rarely exploited due to the difficulty of spin dilution, and π-stacking interaction. In this study, we focus on N,N',N''-tris(2,6-dimethylphenyl)benzenetriimide (BTI-xy), where three xylene moieties connected to the imide groups cover the π-plane of the BTI core. As a result, BTI-xy radical anions without π-stacking interaction were obtained. This led to the slow magnetization relaxation, which is reported for the first time in organic radicals. Furthermore, the relaxation times in a solution state revealed the importance of spin interaction.

Dipolar-Coupled Entangled Molecular 4f Qubits

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

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

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

Modelling Conformational Flexibility in a Spectrally Addressable Molecular Multi-Qubit Model System

Dipolar coupled multi-spin systems have the potential to be used as molecular qubits. Herein we report the synthesis of a molecular multi-qubit model system with three individually addressable, weakly interacting, spin 1 / 2 ${{ 1/2 }}$ centres of differing g-values. We use pulsed Electron Paramagnetic Resonance (EPR) techniques to characterise and separately address the individual electron spin qubits; Cu^II , Cr₇ Ni ring and a nitroxide, to determine the strength of the inter-qubit dipolar interaction. Orientation selective Relaxation-Induced Dipolar Modulation Enhancement (os-RIDME) detecting across the Cu^II spectrum revealed a strongly correlated Cu^II -Cr₇ Ni ring relationship; detecting on the nitroxide resonance measured both the nitroxide and Cu^II or nitroxide and Cr₇ Ni ring correlations, with switchability of the interaction based on differing relaxation dynamics, indicating a handle for implementing EPR-based quantum information processing (QIP) algorithms.

Atomically precise control of rotational dynamics in charged rare-earth complexes on a metal surface

Complexes containing rare-earth ions attract great attention for their technological applications ranging from spintronic devices to quantum information science. While charged rare-earth coordination complexes are ubiquitous in solution, they are challenging to form on materials surfaces that would allow investigations for potential solid-state applications. Here we report formation and atomically precise manipulation of rare-earth complexes on a gold surface. Although they are composed of multiple units held together by electrostatic interactions, the entire complex rotates as a single unit when electrical energy is supplied from a scanning tunneling microscope tip. Despite the hexagonal symmetry of the gold surface, a counterion at the side of the complex guides precise three-fold rotations and 100% control of their rotational directions is achieved using a negative electric field from the scanning probe tip. This work demonstrates that counterions can be used to control dynamics of rare-earth complexes on materials surfaces for quantum and nanomechanical applications.

Rare-earth elements are vital to advanced technological applications ranging from spintronic devices to quantum information science. Here, the authors formed charged rare-earth complexes on a material surface and demonstrated atomically precise control on their rotational dynamics.

Field-Induced Slow Magnetic Relaxation in CoII Cyclopropane-1,1-dicarboxylates

New Co^II substituted malonate field-induced molecular magnets {[Rb₆Co₃(cpdc)₆(H₂O)₁₂]∙6H₂O}_n (1) and [Cs₂Co(cpdc)₂(H₂O)₆]_n (2) (where cpdc²⁻ stands for cyclopropane-1,1-dicarboxylic acid dianions) were synthesized. Both compounds contain mononuclear bischelate fragments {Co^II(cpdc)₂(H₂O)₂}²⁻ where the quasi-octahedral cobalt environment (CoO₆) is complemented by water molecules in apical positions. The alkali metal atoms play the role of connectors between the bischelate fragments to form 3D and 2D polymeric structures for 1 and 2, respectively. Analysis of dc magnetic data using the parametric Griffith Hamiltonian for high-spin Co^II supported by ab initio calculations revealed that both compounds have an easy axis of magnetic anisotropy. Compounds 1 and 2 exhibit slow magnetic relaxation under an external magnetic field (H_DC = 1000 and 1500 Oe, respectively).

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.

Chemical control of spin-lattice relaxation to discover a room temperature molecular qubit

The second quantum revolution harnesses exquisite quantum control for a slate of diverse applications including sensing, communication, and computation. Of the many candidates for building quantum systems, molecules offer both tunability and specificity, but the principles to enable high temperature operation are not well established. Spin-lattice relaxation, represented by the time constant T ₁, is the primary factor dictating the high temperature performance of quantum bits (qubits), and serves as the upper limit on qubit coherence times (T ₂). For molecular qubits at elevated temperatures (>100 K), molecular vibrations facilitate rapid spin-lattice relaxation which limits T ₂ to well below operational minimums for certain quantum technologies. Here we identify the effects of controlling orbital angular momentum through metal coordination geometry and ligand rigidity via π-conjugation on T ₁ relaxation in three four-coordinate Cu²⁺ S = ½ qubit candidates: bis(N,N'-dimethyl-4-amino-3-penten-2-imine) copper(ii) (Me₂Nac)₂ (1), bis(acetylacetone)ethylenediamine copper(ii) Cu(acacen) (2), and tetramethyltetraazaannulene copper(ii) Cu(tmtaa) (3). We obtain significant T ₁ improvement upon changing from tetrahedral to square planar geometries through changes in orbital angular momentum. T ₁ is further improved with greater π-conjugation in the ligand framework. Our electronic structure calculations reveal that the reduced motion of low energy vibrations in the primary coordination sphere slows relaxation and increases T ₁. These principles enable us to report a new molecular qubit candidate with room temperature T ₂ = 0.43 μs, and establishes guidelines for designing novel qubit candidates operating above 100 K.

Three individually addressable spin qubits in a single molecule

An asymmetric bis-phenol-β-diketone (H₄L) has been designed as a ligand programmed to promote the assembly of a molecular arrangement composed of three magnetically exchanged [NiCu] pairs, each exhibiting an S = 1/2 spin. The latter are shown by EPR and magnetometry to be good qubit realizations and non-equivalent within the molecule in the solid state, as required for conditional quantum gates.

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⟩).

Quantum error correction with molecular spin qudits

Molecular multi-level spin qudits are very promising for quantum computing, embedding quantum error correction within single objects. We compare the performance of electronic/nuclear molecular qudits in the implementation of quantum error correction.

Direct detection of spin polarization in photoinduced charge transfer through a chiral bridge

It is well assessed that the charge transport through a chiral potential barrier can result in spin-polarized charges. The possibility of driving this process through visible photons holds tremendous potential for several aspects of quantum information science, e.g., the optical control and readout of qubits. In this context, the direct observation of this phenomenon via spin-sensitive spectroscopies is of utmost importance to establish future guidelines to control photo-driven spin selectivity in chiral structures. Here, we provide direct proof that time-resolved electron paramagnetic resonance (EPR) can be used to detect long-lived spin polarization generated by photoinduced charge transfer through a chiral bridge. We propose a system comprising CdSe quantum dots (QDs), as a donor, and C₆₀, as an acceptor, covalently linked through a saturated oligopeptide helical bridge (χ) with a rigid structure of ∼10 Å. Time-resolved EPR spectroscopy shows that the charge transfer in our system results in a C₆₀ radical anion, whose spin polarization maximum is observed at longer times with respect to that of the photogenerated C₆₀ triplet state. Notably, the theoretical modelling of the EPR spectra reveals that the observed features may be compatible with chirality-induced spin selectivity, but the electronic features of the QD do not allow the unambiguous identification of the CISS effect. Nevertheless, we identify which parameters need optimization for unambiguous detection and quantification of the phenomenon. This work lays the basis for the optical generation and direct manipulation of spin polarization induced by chirality.

Our work provides a first attempt to directly detect the spin polarisation of Chiral-Induced Spin Selectivity (CISS) effect by studying the photoinduced electron transfer in a CdSe Quantum Dot-chiral bridge-fullerene derivative (QD–χ–C₆₀) system.

Synthesis, structure, magnetic properties and thermal behaviour of Ba–MII (MII = Mn, Co, Cu, and Zn) allylmalonates

A series of Ba-MII complexes with allylmalonic acid anions [BaMII(Amal)2(H2O)3]n (MII = Mn, Co, Cu, and Zn) were synthesized. The magnetic measurements revealed slow magnetic relaxation in non-zero field (HDC = 1500 Oe) for CoII ions.

Electron spin resonance of single iron phthalocyanine molecules and role of their non-localized spins in magnetic interactions

Electron spin resonance (ESR) spectroscopy is a crucial tool, through spin labelling, in investigations of the chemical structure of materials and of the electronic structure of materials associated with unpaired spins. ESR spectra measured in molecular systems, however, are established on large ensembles of spins and usually require a complicated structural analysis. Recently, the combination of scanning tunnelling microscopy with ESR has proved to be a powerful tool to image and coherently control individual atomic spins on surfaces. Here we extend this technique to single coordination complexes-iron phthalocyanines (FePc)-and investigate the magnetic interactions between their molecular spin with either another molecular spin (in FePc-FePc dimers) or an atomic spin (in FePc-Ti pairs). We show that the molecular spin density of FePc is both localized at the central Fe atom and also distributed to the ligands (Pc), which yields a strongly molecular-geometry-dependent exchange coupling.

Magnetic anisotropies of Ho(III) and Dy(III) single-molecule magnets experimentally determined via polarized neutron diffraction

We present the magnetic anisotropy of two isostructural pentagonal-bipyramidal complexes, [Ln(H₂O)₅(HMPA)₂]I₃·2HMPA (HMPA = hexamethylphosphoramide, Ln = Dy, Ho). Using ac magnetic susceptibility measurements, we find magnetic relaxation barriers of 600 K and 270 K for the Dy- and Ho-compounds, respectively. This difference is supported by polarized neutron diffraction (PND) measured at 5 K and 1 T which provides the first experimental evidence that the transverse elements in the magnetic anisotropy of the Ho-analogue are significant, whereas the Dy-analogue has a near-axial magnetic anisotropy with vanishing transverse contributions. The coordination geometries of the two complexes are highly similar, and we attribute the loss of strong magnetic axiality as expressed in the atomic susceptibility tensors from PND, as well as the smaller relaxation barrier in the Ho-complex compared to the Dy-complex, to the less favorable interaction of the pentagonal bipyramidal crystal field with the characteristics of the Ho(III) 4f-charge distribution.

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

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

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.

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.

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.

Increasing the Hilbert space dimension using a single coupled molecular spin

Quantum technologies are expected to introduce revolutionary changes in information processing in the near future. Nowadays, one of the main challenges is to be able to handle a large number of quantum bits (qubits), while preserving their quantum properties. Beyond the usual two-level encoding capacity of qubits, multi-level quantum systems are a promising way to extend and increase the amount of information that can be stored in the same number of quantum objects. Recent work (Kues et al. 2017), has shown the possibility to use devices based on photonic integrated circuits to entangle two qudits (with "d" being the number of available states). In the race to develop a mature quantum technology with real-world applications, many possible platforms are being investigated, including those that use photons, trapped ions, superconducting and silicon circuits and molecular magnets. In this work, we present the electronic read-out of a coupled molecular multi-level quantum systems, carried by a single Tb₂Pc₃ molecular magnet. Owning two magnetic centres, this molecular magnet architecture permits a 16 dimensions Hilbert space, opening the possibility of performing more complex quantum algorithms.

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.

Magnetic-Field-Orientation Dependent Thermal Entanglement of a Spin-1 Heisenberg Dimer: The Case Study of Dinuclear Nickel Complex with an Uniaxial Single-Ion Anisotropy

The bipartite entanglement in pure and mixed states of a quantum spin-1 Heisenberg dimer with exchange and uniaxial single-ion anisotropies is quantified through the negativity in a presence of the external magnetic field. At zero temperature the negativity shows a marked stepwise dependence on a magnetic field with two abrupt jumps and plateaus, which can be attributed to the quantum antiferromagnetic and quantum ferrimagnetic ground states. The magnetic-field-driven phase transition between the quantum antiferromagnetic and quantum ferrimagnetic ground states manifests itself at nonzero temperatures by a local minimum of the negativity, which is followed by a peculiar field-induced rise of the negativity observable in a range of moderately strong magnetic fields. The rising temperature generally smears out abrupt jumps and plateaus of the negativity, which cannot be distinguished in the relevant dependencies above a certain temperature. It is shown that the thermal entanglement is most persistent against rising temperature at the magnetic field, for which an energy gap between a ground state and a first excited state is highest. Besides, temperature variations of the negativity of the spin-1 Heisenberg dimer with an easy-axis single-ion anisotropy may exhibit a singular point-kink, at which the negativity has discontinuity in its first derivative. The homodinuclear nickel complex [Ni2(Medpt)2(μ-ox)(H2O)2](ClO4)2·2H2O provides a suitable experimental platform of the antiferromagnetic spin-1 Heisenberg dimer, which allowed us to estimate a strength of the bipartite entanglement between two exchange-coupled Ni2+ magnetic ions on the grounds of the interaction constants reported previously from the fitting procedure of the magnetization data. It is verified that the negativity of this dinuclear compound is highly magnetic-field-orientation dependent due to presence of a relatively strong uniaxial single-ion anisotropy.

A Molecular Approach to Quantum Sensing

The second quantum revolution hinges on the creation of materials that unite atomic structural precision with electronic and structural tunability. A molecular approach to quantum information science (QIS) promises to enable the bottom-up creation of quantum systems. Within the broad reach of QIS, which spans fields ranging from quantum computation to quantum communication, we will focus on quantum sensing. Quantum sensing harnesses quantum control to interrogate the world around us. A broadly applicable class of quantum sensors would feature adaptable environmental compatibility, control over distance from the target analyte, and a tunable energy range of interaction. Molecules enable customizable "designer" quantum sensors with tunable functionality and compatibility across a range of environments. These capabilities offer the potential to bring unmatched sensitivity and spatial resolution to address a wide range of sensing tasks from the characterization of dynamic biological processes to the detection of emergent phenomena in condensed matter. In this Outlook, we outline the concepts and design criteria central to quantum sensors and look toward the next generation of designer quantum sensors based on new classes of molecular sensors.

Exploring Photogenerated Molecular Quartet States as Spin Qubits and Qudits

Photogenerated molecular spin systems hold great promise for applications in quantum information science because they can be prepared in well-defined spin states at modest temperatures, they often exhibit long coherence times, and their properties can be tuned by chemical synthesis. Here, we investigate a molecular spin system composed of a 1,6,7,12-tetra(4-tert-butylphenoxy)perylene-3,4:9,10-bis(dicarboximide) (PDI) chromophore covalently linked to a stable nitroxide radical (TEMPO) by optical and electron paramagnetic resonance (EPR) techniques. Upon photoexcitation of the spin system, a quartet state is formed as confirmed by transient nutation experiments. This quartet state has spin polarization lifetimes longer than 0.1 ms and is characterized by relatively long coherence times of ∼1.8 μs even at 80 K. Rabi oscillation experiments reveal that more than 60 single-qubit logic operations can be performed with this system at 80 K. The large magnitude of the nitroxide ¹⁴N hyperfine coupling in the quartet state of PDI-TEMPO is resolved in the transient EPR spectra and leads to a further splitting of the quartet state electron spin sublevels. We discuss the properties of this photogenerated multilevel system, comprising 12 electron-nuclear spin states, in the context of its viability as a qubit for applications in quantum information science.

Gold(i) bridged dimeric and trimeric heterometallic {Cr7Ni}-based qubit systems and their characterization

Gold(i) bridged dimeric and trimeric structures of a ground state spin S = 1/2 heterometallic {Cr₇Ni} wheel have been prepared and studied by continuous wave (CW) and pulsed wave EPR spectrometry. The {Cr₇Ni} relaxation time constants (T₁ and T_m) show rates matching well with previous observations. Four pulse Double Electron Resonance (DEER) studies suggest presence of more than one conformations. Small Angle X-ray Scattering (SAXS) in conjunction with Molecular Dynamic (MD) Simulations were performed to look at the possible conformations in solution. In line with DEER results, simulation data further indicated more flexible molecular geometry in solution than the one in solid state.

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.

Lanthanoid Complexes as Molecular Materials: The Redox Approach

The development of molecular materials with novel functionality offers promise for technological innovation. Switchable molecules that incorporate redox-active components are enticing candidate compounds due to their potential for electronic manipulation. Lanthanoid metals are most prevalent in their trivalent state and usually redox-activity in lanthanoid complexes is restricted to the ligand. The unique electronic and physical properties of lanthanoid ions have been exploited for various applications, including in magnetic and luminescent materials as well as in catalysis. Lanthanoid complexes are also promising for applications reliant on switchability, where the physical properties can be modulated by varying the oxidation state of a coordinated ligand. Lanthanoid-based redox activity is also possible, encompassing both divalent and tetravalent metal oxidation states. Thus, utilization of redox-active lanthanoid metals offers an attractive opportunity to further expand the capabilities of molecular materials. This review surveys both ligand and lanthanoid centered redox-activity in pre-existing molecular systems, including tuning of lanthanoid magnetic and photophysical properties by modulating the redox states of coordinated ligands. Ultimately the combination of redox-activity at both ligands and metal centers in the same molecule can afford novel electronic structures and physical properties, including multiconfigurational electronic states and valence tautomerism. Further targeted exploration of these features is clearly warranted, both to enhance understanding of the underlying fundamental chemistry, and for the generation of a potentially important new class of molecular material.

When Molecular Magnetism Meets Supramolecular Chemistry: Multifunctional and Multiresponsive Dicopper(II) Metallacyclophanes as Proof-of-Concept for Single-Molecule Spintronics and Quantum Computing Technologies?

Molecular magnetism has made a long journey, from the fundamental studies on through-ligand electron exchange magnetic interactions in dinuclear metal complexes with extended organic bridges to the more recent exploration of their electron spin transport and quantum coherence properties. Such a field has witnessed a renaissance of dinuclear metallacyclic systems as new experimental and theoretical models for single-molecule spintronics and quantum computing, due to the intercrossing between molecular magnetism and metallosupramolecular chemistry. The present review reports a state-of-the-art overview as well as future perspectives on the use of oxamato-based dicopper(II) metallacyclophanes as promising candidates to make multifunctional and multiresponsive, single-molecule magnetic (nano)devices for the physical implementation of quantum information processing (QIP). They incorporate molecular magnetic couplers, transformers, and wires, controlling and facilitating the spin communication, as well as molecular magnetic rectifiers, transistors, and switches, exhibiting a bistable (ON/OFF) spin behavior under external stimuli (chemical, electronic, or photonic). Special focus is placed on the extensive research work done by Professor Francesc Lloret, an outstanding chemist, excellent teacher, best friend, and colleague, in recognition of his invaluable contributions to molecular magnetism on the occasion of his 65th birthday.

Exploring the Organometallic Route to Molecular Spin Qubits: The [CpTi(cot)] Case

The coherence time of the 17-electron, mixed sandwich complex [CpTi(cot)], (η⁸ -cyclooctatetraene)(η⁵ -cyclopentadienyl)titanium, reaches 34 μs at 4.5 K in a frozen deuterated toluene solution. This is a remarkable coherence time for a highly protonated molecule. The intramolecular distances between the Ti and H atoms provide a good compromise between instantaneous and spin diffusion sources of decoherence. Ab initio calculations at the molecular and crystal packing levels reveal that the characteristic low-energy ring rotations of the sandwich framework do not yield a too detrimental spin-lattice relaxation because of their small spin-phonon coupling. The volatility of [CpTi(cot)] and the accessibility of the semi-occupied, non-bonding d z 2 orbital make this neutral compound an ideal candidate for single-qubit addressing on surface and quantum sensing in combination with scanning probe microscopy.

A dissymmetric [Gd2] coordination molecular dimer hosting six addressable spin qubits

Artificial magnetic molecules can host several spin qubits, which could then implement small-scale algorithms. In order to become of practical use, such molecular spin processors need to increase the available computational space and warrant universal operations. Here, we design, synthesize and fully characterize dissymetric molecular dimers hosting either one or two Gadolinium(III) ions. The strong sensitivity of Gadolinium magnetic anisotropy to its local coordination gives rise to different zero-field splittings at each metal site. As a result, the [LaGd] and [GdLu] complexes provide realizations of distinct spin qudits with eight unequally spaced levels. In the [Gd₂] dimer, these properties are combined with a Gd-Gd magnetic interaction, sufficiently strong to lift all level degeneracies, yet sufficiently weak to keep all levels within an experimentally accessible energy window. The spin Hamiltonian of this dimer allows a complete set of operations to act as a 64-dimensional all-electron spin qudit, or, equivalently, as six addressable qubits. Electron paramagnetic resonance experiments show that resonant transitions between different spin states can be coherently controlled, with coherence times T_M of the order of 1 µs limited by hyperfine interactions. Coordination complexes with embedded quantum functionalities are promising building blocks for quantum computation and simulation hybrid platforms.

Trigonal Bipyramidal V3+ Complex as an Optically Addressable Molecular Qubit Candidate

Synthetic chemistry enables a bottom-up approach to quantum information science, where atoms can be deterministically positioned in a quantum bit or qubit. Two key requirements to realize quantum technologies are qubit initialization and read-out. By imbuing molecular spins with optical initialization and readout mechanisms, analogous to solid-state defects, molecules could be integrated into existing quantum infrastructure. To mimic the electronic structure of optically addressable defect sites, we designed the spin-triplet, V3+ complex, (C6F5)3trenVCNtBu (1). We measured the static spin properties as well as the spin coherence time of 1 demonstrating coherent control of this spin qubit with a 240 GHz electron paramagnetic resonance spectrometer powered by a free electron laser. We found that 1 exhibited narrow, near-infrared photoluminescence (PL) from a spin-singlet excited state. Using variable magnetic field PL spectroscopy, we resolved emission into each of the ground-state spin sublevels, a crucial component for spin-selective optical initialization and readout. This work demonstrates that trigonally symmetric, heteroleptic V3+ complexes are candidates for optical spin addressability.

Optically addressable molecular spins for quantum information processing

Spin-bearing molecules are promising building blocks for quantum technologies as they can be chemically tuned, assembled into scalable arrays, and readily incorporated into diverse device architectures. In molecular systems, optically addressing ground-state spins would enable a wide range of applications in quantum information science, as has been demonstrated for solid-state defects. However, this important functionality has remained elusive for molecules. Here, we demonstrate such optical addressability in a series of synthesized organometallic, chromium(IV) molecules. These compounds display a ground-state spin that can be initialized and read out using light and coherently manipulated with microwaves. In addition, through atomistic modification of the molecular structure, we vary the spin and optical properties of these compounds, indicating promise for designer quantum systems synthesized from the bottom-up.