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

Nutation Spectroscopy of a Weakly Interacting Heterobimetallic Spin System

The use of VIV and CuII spins to design weakly coupled and dissymmetric spin systems has been examined. Such systems were synthesized using porphyrin-based complexes, with external coordination sites allowing for the formation of dimers via a PdII linker ion. Continuous-wave (CW) Electron Paramagnetic Resonance (EPR) spectroscopy allowed the unequivocal magnetic characterization of the mononuclear precursors VO and Cu. The porphyrin dimer (VO)PdCu presented a broad and overlapped spectrum that was more pronounced than for the previously reported (VO)Pd(VO), hinting at the effect of weak interspin interactions between dissimilar spins. Pulsed EPR experiments on VO, (VO)Pd(VO) and (VO)PdCu samples diluted in a diamagnetic matrix confirmed that this complication is also present in the Field-Swept Echo-Detected (FSED) spectra of the heterometallic (VO)PdCu system. Despite the strongly overlapped field-swept spectra, spin nutation experiments revealed two distinct oscillations in the case of (VO)PdCu, which are assigned to transitions with different spin characters. Remarkably, coherence is retained above liquid nitrogen temperatures for all complexes, in particular up to 295 K for VO and (VO)Pd(VO) and 150 K for (VO)PdCu.

Room-Temperature Optical Spin Polarization of an Electron Spin Qudit in a Vanadyl-Free Base Porphyrin Dimer

Photoexcited organic chromophores appended to molecular qubits can serve as a source of spin initialization or multilevel qudit generation for quantum information applications. So far, this approach has been primarily investigated in chromophore-stable radical systems. Here, we extend this concept to a meso-meso linked oxovanadium(IV) porphyrin-free-base porphyrin dimer. Femtosecond transient absorption experiments reveal that photoexcitation of the free-base porphyrin leads to picosecond triplet state formation via enhanced intersystem crossing. Time-resolved electron paramagnetic resonance (TREPR) experiments carried out at both 85 K and room temperature reveal the formation of a long-lived spin-polarized quartet state through triplet-doublet spin mixing. Notably, a distinct hyperfine structure arising from the interaction between the electron spin quartet state and the vanadyl nucleus (51V, I = 7/2) is evident, with the quartet state showing long-lived spin polarization even at room temperature. Theoretical simulations of the TREPR spectra confirm the photogenerated quartet state and provide insights into the non-Boltzmann spin populations. Exploiting this phenomenon affords the possibility of using photoinduced triplet states in porphyrins for quantum information as a resource to polarize and magnetically couple molecular electronic or nuclear spin qubits and qudits.

Asymmetric [Dy2] molecules deposited into micro-SQUID susceptometers: in situ characterization of their magnetic integrity

The controlled integration of magnetic molecules into superconducting circuits is key to developing hybrid quantum devices. Herein, we study [Dy2] molecular dimers deposited into micro-SQUID susceptometers. The results of magnetic, heat capacity and magnetic resonance experiments, backed by theoretical calculations, show that each [Dy2] dimer fulfills the main requisites to encode a two-spin quantum processor. Arrays of between 2 × 108 and 7 × 109[Dy2] molecules were optimally integrated under ambient conditions inside the 20 μm wide loops of micro-SQUID sensors by means of dip-pen nanolithography. Equilibrium magnetic susceptibility and phonon-assisted spin tunneling dynamics measured in situ substantiate that these molecules preserve spin ground states, magnetic interactions and magnetic asymmetry that characterize them in bulk. These results show that it is possible to interface multi-qubit molecular complexes with on-chip superconducting circuits without disturbing their relevant properties and suggest the potential of soft nanolithography techniques to achieve this goal.

Fault-tolerant computing with single-qudit encoding in a molecular spin

We show that molecular spins represent ideal materials to realize a fault-tolerant quantum computer, in which all quantum operations include protection against leading (dephasing) errors. This is achieved by pursuing a qudit approach, in which logical error-corrected qubits are encoded in a single multi-level molecule (a qudit) and not in a large collection of two-level systems, as in standard codes. By preventing such an explosion of resources, this emerging way of thinking about quantum error correction makes its actual implementation using molecular spins much closer. We show how to perform all quantum computing operations (logical gates, corrections and measurements) without propagating errors. We achieve a quasi-exponential error correction with only linear qudit size growth, i.e. a higher efficiency than the standard approach based on stabilizer codes and concatenation.

Osmium(III) Acetylacetonate and Its Missing Polymorph: A Magnetic and Structural Investigation

Despite the potential for their application, the magnetic behavior of complexes containing 4d and 5d metal ions is underexplored, evidencing the need for benchmark multi-technique studies on simple molecules. We report here a structural and magnetic study on osmium(III) acetylacetonate [Os(acac)3]. X-ray single crystal diffraction did not allow us to determine the structure of the β-polymorph of [Os(acac)3]. The combined magnetic (dc magnetic measurements on powder and cantilever torque magnetometry on single crystal) and spectroscopic (electron paramagnetic resonance, EPR) characterization is here used to provide further evidence that its structure is indeed the one of the orthorhombic "missing polymorph", analogous to the ruthenium(III) derivative. Our study shows that all acetylacetonate complexes of the eighth group of the periodic table show dimorphism and are isomorphic. The EPR characterization allowed the experimental assessment of the easy axis nature of the ground doublet and the determination of the first hyperfine coupling in an osmium complex. Torque magnetometry, applied here for the first time on an osmium-based molecule, determined the orientation of the easy axis along the pseudo C3 axis of the complex. Ac magnetometric measurements revealed in-field slow relaxation of the magnetization further slowed by the suppression of dipolar fields via magnetic dilution in the isostructural gallium(III) analogue.

Coherent spin-control of S = 1 vanadium and molybdenum complexes

The burgeoning field of quantum sensing hinges on the creation and control of quantum bits. To date, the most well-studied quantum sensors are optically active, paramagnetic defects residing in crystalline hosts. We previously developed analogous optically addressable molecules featuring a ground-state spin-triplet centered on a Cr4+ ion with an optical-spin interface. In this work, we evaluate isovalent V3+ and Mo4+ congeners, which offer unique advantages, such as an intrinsic nuclear spin for V3+ or larger spin-orbit coupling for Mo4+, as optically addressable spin systems. We assess the ground-state spin structure and dynamics for each complex, illustrating that all of these spin-triplet species can be coherently controlled. However, unlike the Cr4+ derivatives, these pseudo-tetrahedral V3+ and Mo4+ complexes exhibit no measurable emission. Coupling absorption spectroscopy with computational predictions, we investigate why these complexes exhibit no detectable photoluminescence. These cumulative results suggest that design of future V3+ complexes should target pseudo-tetrahedral symmetries using bidentate or tridentate ligand scaffolds, ideally with deuterated or fluorinated ligand environments. We also suggest that spin-triplet Mo4+, and by extension W4+, complexes may not be suitable candidate optically addressable qubit systems due to their low energy spin-singlet states. By understanding the failures and successes of these systems, we outline additional design features for optically addressable V- or Mo-based molecules to expand the library of tailor-made quantum sensors.

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.

Photoinduced Magnetic Exchange-Jump Promotes Ground State Biradical Electron Spin Polarization

Photoinduced electron spin polarization (ESP) is reported in the electronic ground states of three Pt(II) complexes comprised of two S = 1/2 nitronyl nitroxide (NN) radicals attached through different length para-phenylethynyl bridges to the 3,6 positions of a catecholate (CAT, donor) and 4,4'-di-tert-butyl-2,2'-bipyridine (bpy, acceptor). Complexes 1-3 have from 17 to 41 bonds separating NN radicals and display cw-EPR spectra consistent with |JNN-NN| ≫ |aN|, |JNN-NN| ≥ |aN|, and |JNN-NN| < |aN|, respectively, where JNN-NN is the magnetic exchange coupling between NN radicals in the electronic ground state, and aN is the isotropic 14N hyperfine coupling constant. Light-induced transient EPR spectra characterized as enhanced ground-state absorption were observed for all three complexes using 532 nm pulsed laser excitation into the ligand-to-ligand charge transfer (LL'CT) band of the (CAT)Pt(bpy) chromophore. The magnitude of the observed ESP increases in the order 1 < 2 < 3 and is inversely correlated with the magnitude of ground-state JNN-NN. In addition to the experimental observation of net absorptive polarization in 1-3, light excitation also produces multiplet polarization in 2. Since the weak dipolar coupling leads to a strong spectral overlap of the absorptive and emissive components, the multiplet polarization is not observed in 1 and 3 and is very weak in 2. The ability to spin-polarize multiple radical spins with a single photon is anticipated to advance new photoinduced multi qubit/qudit ESP protocols for quantum information science applications.

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.

Quantum spin coherence and electron spin distribution channels in vanadyl-containing lantern complexes

We herein investigate the heterobimetallic lantern complexes [PtVO(SOCR)4] as charge neutral electronic qubits based on vanadyl complexes (S = 1/2) with nuclear spin-free donor atoms. The derivatives with R = Me (1) and Ph (2) give highly resolved X-band EPR spectra in frozen CH2Cl2/toluene solution, which evidence the usual hyperfine coupling with the 51V nucleus (I = 7/2) and an additional superhyperfine interaction with the I = 1/2 nucleus of the 195Pt isotope (natural abundance ca. 34%). DFT calculations ascribe the spin density delocalization on the Pt2+ ion to a combination of π and δ pathways, with the former representing the predominant channel. Spin relaxation measurements in frozen CD2Cl2/toluene-d8 solution between 90 and 10 K yield Tm values (1-6 μs in 1 and 2-11 μs in 2) which compare favorably with those of known vanadyl-based qubits in similar matrices. Coherent spin manipulations indeed prove possible at 70 K, as shown by the observation of Rabi oscillations in nutation experiments. The results indicate that the heavy Group 10 metal ion is not detrimental to the coherence properties of the vanadyl moiety and that Pt-VO lanterns can be used as robust spin-coherent building blocks in materials science and quantum technologies.

How to Cross an Energy Barrier at Zero Kelvin without Tunneling Effect

This Letter deals with the broad class of magnetic systems having a single or collective spin S with an energy barrier, such as rare-earth elements and their compounds, single molecule magnets with uniaxial anisotropy, and more generally any other anisotropic quantum system made of single or multiple objects with discrete energy levels. Till now, the reversal of the magnetization of such systems at zero kelvin required making use of quantum tunneling with a significant transverse field or transverse anisotropy term, at resonance. Here, we show that another very simple method exists. It simply consists in the application of a particular sequence of electromagnetic radiations in the ranges of optical or microwave frequencies, depending on the characteristics of the system (spin and anisotropy values for magnetic systems). This produces oscillations of the Rabi type that pass above the barrier, thus extending these oscillations between the two energy wells with mixtures of all the 2S+1 states. In addition to its basic character, this approach opens up new directions of research in quantum information with possible breakthroughs in the current use of multiple quantum bits.

Impact of ligand chlorination and counterion tuning on high-field spin relaxation in a series of V(IV) complexes

Methods of controlling spin coherence by molecular design are essential to efforts to develop molecular qubits for quantum information and sensing applications. In this manuscript, we perform the first studies of how arrangements of ^35/37Cl nuclear spins in the ligand shell and counterion selection affect the coherent spin dynamics of V(IV) complexes at a high magnetic field. We prepared eight derivatives of the vanadium triscatecholate complex with varying arrangements of ^35/37Cl substitution on the catechol backbone and R₃NH⁺ counterions (R = Et, n-Bu, n-Hex) and investigated these species via structural and spectroscopic methods. Hahn-echo pulsed electron paramagnetic resonance (EPR) experiments at high-frequency (120 GHz) and field (ca. 4.4 T) were used to extract the phase-memory relaxation time (T_m) and spin-lattice relaxation (T₁) times of the series of complexes. We found T_m values ranging from 4.8 to 1.1 μs in the temperature range of 5 to 40 K, varying by approximately 20% as a function of substitutional pattern. In-depth analysis of the results herein and comparison with related studies of brominated analogues disproves multiple hypothesized mechanisms for T_m control. Ultimately, we propose that more specific properties of the halogen atoms, e.g. the chemical shift, V⋯Cl hyperfine coupling, and quadrupolar coupling, could be contributing to the V(IV) T_m time.

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.

Modular Approach to Creating Functionalized Surface Arrays of Molecular Qubits

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

Quantum Mimicry With Inorganic Chemistry

Quantum objects, such as atoms, spins, and subatomic particles, have important properties due to their unique physical properties that could be useful for many different applications, ranging from quantum information processing to magnetic resonance imaging. Molecular species also exhibit quantum properties, and these properties are fundamentally tunable by synthetic design, unlike ions isolated in a quadrupolar trap, for example. In this comment, we collect multiple, distinct, scientific efforts into an emergent field that is devoted to designing molecules that mimic the quantum properties of objects like trapped atoms or defects in solids. Mimicry is endemic in inorganic chemistry and featured heavily in the research interests of groups across the world. We describe a new field of using inorganic chemistry to design molecules that mimic the quantum properties (e.g. the lifetime of spin superpositions, or the resonant frequencies thereof) of other quantum objects, "quantum mimicry." In this comment, we describe the philosophical design strategies and recent exciting results from application of these strategies.

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, spin1 / 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; CuII , 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 CuII spectrum revealed a strongly correlated CuII -Cr7 Ni ring relationship; detecting on the nitroxide resonance measured both the nitroxide and CuII 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.

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.

Theoretical Design of Optimal Molecular Qudits for Quantum Error Correction

We pinpoint the key ingredients ruling decoherence in multispin clusters, and we engineer the system Hamiltonian to design optimal molecules embedding quantum error correction. These are antiferromagnetically coupled systems with competing exchange interactions, characterized by many low-energy states in which decoherence is dramatically suppressed and does not increase with the system size. This feature allows us to derive optimized code words, enhancing the power of the quantum error correction code by orders of magnitude. We demonstrate this by a complete simulation of the system dynamics, including the effect of decoherence driven by a nuclear spin bath and the full sequence of pulses to implement error correction and logical gates between protected states.

Nanomaterials for Quantum Information Science and Engineering

Quantum information science and engineering (QISE)-which entails the use of quantum mechanical states for information processing, communications, and sensing-and the area of nanoscience and nanotechnology have dominated condensed matter physics and materials science research in the 21st century. Solid-state devices for QISE have, to this point, predominantly been designed with bulk materials as their constituents. This review considers how nanomaterials (i.e., materials with intrinsic quantum confinement) may offer inherent advantages over conventional materials for QISE. The materials challenges for specific types of qubits, along with how emerging nanomaterials may overcome these challenges, are identified. Challenges for and progress toward nanomaterials-based quantum devices are condidered. The overall aim of the review is to help close the gap between the nanotechnology and quantum information communities and inspire research that will lead to next-generation quantum devices for scalable and practical quantum applications.

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.