Long Coherence Times in Nuclear Spin-Free Vanadyl Qubits

Interactions between well-isolated Dy3+ ions considerably contribute to the demagnetization of a mononuclear acetylacetonate-pyrazinate complex

A series of new mononuclear square antiprismatic complexes comprising acetylacetonate (acac-), pyrazine-2-carboxylate (PyrCOO-) and 1,10-phenanthroline (phen) ligands, namely, [Ln(acac)2(PyrCOO)(phen)] (Ln is Dy-Yb, Y; 1-5, 6), was prepared and studied. These complexes are new examples of extremely scarcely studied eight-coordinated tetra-chelate complexes comprising β-diketonate and carboxylate ligands. Complexes 1, 3 and 5 exhibit pronounced slowdown of demagnetization, with corresponding pathways additionally validated by ab initio calculations. In particular, complex 1 exhibits zero-field relaxation with a Δeff/kB of 149 K, while the application of an optimal DC field (1500 Oe) enhances the Δeff/kB value to 265 K. Thus, although the quantum tunneling of magnetization (QTM) contributes to zero-field relaxation of complex 1, this complex is among the most efficient zero-field Dy-based SMMs formed by β-diketonate and/or carboxylate ligands. Moreover, the Δeff/kB value of 1 under the optimal field is the highest among the related complexes. Interestingly, the Dy-Dy magnetic interactions have a considerable effect on the SMM performance of 1, despite on the spatial (>8 Å) separation of Dy3+ ions isolated by coats of bulky diamagnetic ligands.

Molecular Design for Optically Induced Magnetization: Targeting Excited State Orbital Degeneracy in Tungsten(V) Complexes

The rise of quantum information science has spurred chemists to prepare new molecules that serve as useful building blocks in quantum technologies of the future. Implementation of molecular spin-based qubits requires new methods to induce high spin polarization of samples. Herein, we report design criteria to develop axially symmetric spin-1/2 molecules amenable to optically induced magnetization (OIM), a technique using circularly polarized (CP) excitation to deliver spin polarization. We apply these criteria to develop a series of tungsten(V) chalcogenide complexes that are demonstrated to have large spin-sensitive responses to CP light using magnetic circular dichroism (MCD) that could allow up to ∼20% spin polarization through OIM. Pulsed electron paramagnetic resonance (EPR) spectra reveal these systems have improved relaxation times over molecules like K2IrCl6, a species recently investigated by OIM, and field-swept electron spin-echo (FS-ESE) experiments show they have a remarkable lack of anisotropy in their phase-memory Tm times. The design criteria are general and point toward future ways to improve OIM-initializable qubits.

Conclusive Insight into the Coordination Complexes of a Flexible Bis(β-diketonato) Ligand and Their Phase-Dependent Structure: A Multi-Technique Approach

Multichelating ligands with nuclear spin-free donor atoms are of particular interest for creating stable electronic spin qubits based on paramagnetic transition metal ions. We recently focused on the coordinating ability of the bis(β-diketonato) ligand bdhb2-, featuring two "acac" moieties connected through a 1,3-phenylene bridge (H2bdhb = 1,3-bis(3,5-dioxo-1-hexyl)benzene). The two crystalline complexes of bdhb2- so far isolated and structurally characterized, namely [(VO)2(bdhb)2] (1) and [Co2(bdhb)2(py)4] (2), are dimeric and contain bridging bdhb2- ligands; however, they become mononuclear and quasi-macrocyclic in organic solution. To investigate this unique structural isomerism by high-resolution 1H NMR spectroscopy, we have now synthesized a diamagnetic Zn2+ analogue of 1 and 2, namely [Zn2(bdhb)2(py)2] (3). Although both 2 and 3 are dimeric and contain the same ligands, 3 features only one pyridine molecule per metal ion, whose coordination geometry is square pyramidal rather than tetragonally elongated octahedral. The ESI-MS spectra of 3 in THF and CH2Cl2 contain peaks from both monomeric and dimeric species. However, molecular weight determinations by DOSY and conformational studies based on J-coupling analysis and DFT calculations conclusively prove the rearrangement of 3 into quasi-macrocyclic monomers in THF-d8 and CD2Cl2 solution at room temperature.

Anisotropy of Spin-Lattice Relaxation Time (T1) for Oxo-Vanadium(IV) and Nitrido Chromium(V) Porphyrins

Designing molecular complexes as qubits requires understanding properties that contribute to long electron spin-lattice relaxation times. Spin-lattice relaxation was measured as a function of temperature and position in the spectrum for vanadyl tetraphenylporphyrin (VOTPP) in titanyl tetraphenylporphyin (TiOTPP) and zinc tetraphenylporphyrin (ZnTPP) hosts and for nitrido chromium(V) TPP in TiOTPP. T1 also was measured for the vanadyl complexes of octaethylporphyrin (OEP) and tetratolylporphyrin (TTP) in ZnOEP or ZnTTP, respectively. T1 anisotropy is defined as the ratio of T1 when the magnetic field is along the VO or CrN bond (the z axis) to T1 when the magnetic field is in the porphyrin plane. For these vanadyl and Cr(V) porphyrins, T1 anisotropy increases rapidly between about 60 and 140 K and is strongly dependent on the host lattice, ranging from the unusually large maxima of 36 for VOTPP in TiOTPP and 28 for CrNTPP in TiOTPP to 3.8 for VOTPP in ZnTPP and 3.3 for VOOEP in ZnOEP. Empirical modeling of the temperature dependence of T1 showed that phonons with energies of 170 to 225 cm-1 made substantially larger contributions to relaxation in the perpendicular plane than along the z axis and that the magnitudes of these contributions were strongly dependent on the host lattice. These results demonstrate that optimizing molecules as qubits requires consideration of interaction with the host lattice in addition to molecular properties.

Tunable Spin Qubit Pairs in Quantum Dot-Molecule Conjugates

Organic molecules and quantum dots (QDs) have both shown promise as materials that can host quantum bits (qubits). This is in part because of their synthetic tunability. The current work employs a combination of both materials to demonstrate a series of tunable quantum dot-organic molecule conjugates that can both host photogenerated spin-based qubit pairs (SQPs) and sensitize molecular triplet states. The photogenerated qubit pairs, composed of a spin-correlated radical pair (SCRP), are particularly intriguing since they can be initialized in well-defined, nonthermally populated, quantum states. Additionally, the radical pair enables charge recombination to a polarized molecular triplet state, also in a well-defined quantum state. The materials underlying this system are an organic molecular chromophore and electron donor, 9,10-bis(phenylethynyl)anthracene, and a quantum dot acceptor composed of ZnO. We prepare a series of quantum dot-molecule conjugates that possess variable quantum dot size and two different linker lengths connecting the two moieties. Optical spectroscopy revealed that the QD-molecule conjugates undergo photoexcited charge separation to generate long-lived charge-separated radical pairs. The resulting spin states are probed using light-induced time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy, revealing the presence of singlet-generated SCRPs and molecular triplet states. Notably, the EPR spectra of the radical pairs are dependent on the geometry of this highly tunable system. The g value of the ZnO QD anion is size tunable, and the line widths are influenced by radical pair separation. Overall, this work demonstrates the power of synthetic tunability in adjusting the spin specific addressability, satisfying a key requirement of functional qubit systems.

Effect of Chemical Modification in Trigonal Gd(III) Molecular Qubits

Molecular quantum bits (qubits) are often hailed for the tunability of their properties through chemical backbone modifications. This concept has been explored in detail for transition metal-based systems. However, the effect of chemical modifications in the ligand backbone on the spin dynamics of 4f molecular qubits remains relatively unexplored. We present herein a study of the effect of the addition, and topology thereof, of methoxy groups in the ligand backbone of a Gd(III) qubit while maintaining the molecular symmetry. Continuous wave X-band Electron Paramagnetic Resonance measurements on single crystals of two such derivatized Gd-based molecular qubits provide detailed information on their eigenvector composition. Their dynamic properties were examined by pulse electron paramagnetic resonance on single crystals, revealing that both complexes display coherent spin dynamics up to 100 K, where spin-lattice relaxation limits the coherence. Furthermore, we show that tuning of the ligand field-derived anisotropy leads to control of the eigenvector composition, which translates to control of the Rabi nutation frequency and hence of the time for quantum gate implementation. This demonstrates that molecular qubits offer the possibility for synthetic control and tuning of the speed of coherent manipulations.

Spin coherence phenomena of an S = 1/2 copper(II) system in a polyoxometalate with a less-abundant nuclear spin

The spin coherence phenomena of a system consisting of a mononuclear 3d transition metal S = 1/2 centre embedded in a polyoxometalate with low nuclear-spin abundance, [(n-C4H9)4N]4H2[SiW11O39Cu0.01Zn0.99], have been revealed for the first time. Variable-temperature Hahn-echo experiments using the pulsed electron spin resonance technique showed that its coherence lifetime remains at the submicrosecond level even above 100 K.

The role of electronic excited states in the spin-lattice relaxation of spin-1/2 molecules

Magnetic resonance is a prime method for the study of chemical and biological structures and their dynamical processes. The interpretation of many of these experiments relies on understanding how the spin of unpaired electrons exchanges energy with their environment, or lattice, and relaxes to equilibrium. Here, we overcome the common use of effective spin Hamiltonians to describe spin-lattice relaxation in spin-1/2 and apply ab initio open quantum systems theory to their full molecular electronic wavefunction. Simulations for two Cr(V) coordination compounds under this framework show a marked improvement in accuracy and demonstrate that relaxation in spin-1/2 molecules is enabled by virtual transitions to molecular excited states with energy approaching 20,000 cm-1. This work establishes a connection between the original theory of Van Vleck and modern electronic structure methods, ultimately exemplifying the urgency of further advancing an ab initio approach to spin-lattice relaxation.

Light-induced electron spin qubit coherences in the purple bacteria reaction center protein

Photosynthetic reaction center proteins (RCs) provide ideal model systems for studying quantum entanglement between multiple spins, a quantum mechanical phenomenon wherein the properties of the entangled particles become inherently correlated. Following light-generated sequential electron transfer, RCs generate spin-correlated radical pairs (SCRPs), also referred to as entangled spin qubit (radical) pairs (SQPs). Understanding and controlling coherence mechanisms in SCRP/SQPs is important for realizing practical uses of electron spin qubits in quantum sensing applications. The bacterial RC (bRC) provides an experimental system for exploring quantum effects in the SCRP P865+ QA-, where P865, a special pair of bacteriochlorophylls, is the primary donor, and QA is the primary quinone acceptor. In this study, we focus on understanding how local molecular environments and isotopic substitution, particularly deuteration, influence spin coherence times (TM). Using high-frequency electron paramagnetic resonance (EPR) spectroscopy, we observed that the local environment surrounding P865 and QA plays a significant role in determining TM. Our findings show that while deuteration led to a modest increase in TM, particularly at low temperatures, but the effect was substantially smaller than predicted by classical nuclear spin diffusion alone. This result is in contrast to our previous study of the photosystem I (PSI) RC, where no increase in TM was observed upon deuteration. Theoretical modeling identified several methyl groups at key distances from the spin centers of both bRC and PSI, and methyl group tunneling at low temperatures has been previously suggested as a mechanism for enhanced spin decoherence. Additionally, our study revealed a strong dependence of spin coherence on the orientation of the external magnetic field, highlighting the influence of the protein microenvironment on spin dynamics. These results offer new insights for optimizing coherence times in quantum system design for quantum information science and sensing applications.

Localized Nanoscale Formation of Vanadyl Porphyrin 2D MOF Nanosheets and Their Optimal Coupling to Lumped Element Superconducting Resonators

A strategy toward the realization of a quantum spin processor involves the coupling of spin qubits and qudits to photons within superconducting resonators. To enable the realization of such hybrid architecture, here we first explore the design of a chip with multiple lumped-element LC superconducting resonators optimized for their coupling to distinct transitions of a vanadyl porphyrin electronuclear qudit. The controlled integration of the vanadyl qudit onto the superconducting device, both in terms of number and orientation, is then attained using the in situ formation of nanosheets of a 2D framework built on the vanadyl qudit as a node. Low-temperature transmission experiments demonstrate the coupling of photons in resonators with different frequencies to the targeted electronuclear transitions of the vanadyl qudit, also confirming the control over the vanadyl qudit node orientation. The derived collective spin-photon couplings in the 0.3-1.6 MHz range then allow to estimate enhanced, optimal, single spin photon couplings up to 4 Hz.

A self-assembled metallo-macrocycle two-qubit spin system

A self-assembled, charge-neutral dicopper(II) metallo-macrocycle with a near degenerate singlet-triplet ground state is a prototype molecular two-qubit system. The weakly-coupled spin centres delivered a long phase memory time of 5.4 μs, and each spin can be selectively switched using an applied potential providing a convenient means to modulate the quantum levels.

Phononic modulation of spin-lattice relaxation in molecular qubit frameworks

The solid-state integration of molecular electron spin qubits could promote the advancement of molecular quantum information science. With highly ordered structures and rational designability, microporous framework materials offer ideal matrices to host qubits. They exhibit tunable phonon dispersion relations and spin distributions, enabling optimization of essential qubit properties including the spin-lattice relaxation time (T1) and decoherence time. In this study, through spin dynamic and vibrational spectroscopic characterizations of two radical-embedded framework materials, we show that hydrogen-bonded networks give rise to a low Debye temperature of acoustic phonons and generates sub-terahertz optical phonons, both of which facilitate spin-lattice relaxation. Whereas deuterating hydrogen-bonded networks reduces both phonon frequencies and T1, eliminating such flexible structural motifs raises phonon dispersions and improves the T1 by one to two orders of magnitude. The phononic tunability of spin-lattice relaxation in molecular qubit frameworks would facilitate the development of solid-state qubits operating at elevated temperatures.

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.

Probing decoherence in molecular 4f qubits

We probe herein the fundamental factors that induce decoherence in ensembles of molecular magnetic materials. This is done by pulse Electron Paramagnetic Resonance measurements at X-band (∼9.6 GHz) on single crystals of Gd@Y(trensal) at 0.5, 10-1, 10-2 and 10-3% doping levels, using Hahn echo, partial refocusing and CPMG sequences. The phase memory time, T m, obtained by the Hahn echo sequence at X-band is compared to the one previously determined at higher frequency/magnetic field (∼240 GHz). The combined information from these experiments allows to gain insight into the contributions to decoherence originating from various relaxation mechanisms such as spin-lattice relaxation, electron and nuclear spin diffusion and instantaneous diffusion. We show that while at high magnetic fields T m is limited by spin-lattice relaxation seemingly attributed to a direct process, at lower fields the limiting factor is spectral diffusion. At X-band, for Gd@Y(trensal) we determine a T m in the range 1-12 μs, at 5 K, depending on the magnetic field and concentration of Gd(trensal) in the isostructural diamagnetic host Y(trensal). Importantly, Gd@Y(trensal) displays measurable coherence at temperatures above liquid nitrogen ones, with 125 K being the upper limit. At the lowest dilution level of 10-3% and under dynamic decoupling conditions, the ratio of T m versus the time it takes to implement a quantum gate, T G, reaches the order of 104, in the example of a single qubit π-rotation, which corresponds to an upper limit of gate fidelity of the order of 99.99%, reaching thus the lower limit of qubit figure of merit required for implementations in quantum information technologies.

Enhancing Photogenerated Radical Pair Properties in Donor-Chromophore-Acceptor Systems for Quantum Information Applications

We report on new donor-chromophore-acceptor triads BDX-ANI-NDI and BDX-ANI-xy-NDI where the BDX donor is 2,2,6,6-tetramethylbenzo[1,2-d;4,5-d]bis[1,3]dioxole, the ANI chromophore is 4-(N-piperidinyl)naphthalene-1,8-dicarboximide, the NDI acceptor is naphthalene-1,8:4,5-bis(dicarboximide), and xy is a 2,5-xylyl spacer. The results on these compounds are compared to the analogous derivatives having a p-methoxyaniline (MeOAn) as the donor. BDX•+ has no nitrogen atoms and only a single hydrogen atom coupled to its unpaired electron spin, and therefore has significantly decreased hyperfine interactions compared to MeOAn•+. We use femtosecond transient absorption (fsTA) and nanosecond TA (nsTA) spectroscopies, the latter with an applied static magnetic field, to study the charge transfer dynamics and determine the spin-spin exchange interaction (J) for BDX•+-ANI-NDI•- and BDX•+-ANI-xy-NDI•- at both ambient and cryogenic temperatures. Time-resolved electron paramagnetic resonance (EPR) and pulse-EPR measurements on these spin-correlated radical pairs (SCRPs) were used to probe their spin dynamics. We demonstrate that BDX•+-ANI-xy-NDI•- has an unusually long lifetime of ∼550 μs in glassy butyronitrile (PrCN) at 85 K, which makes it useful for pulse-EPR studies that target quantum information science (QIS) applications. We also show that rotation of the BDX group about the single bond linking it to the neighboring phenyl group has a significant impact on the spin dynamics, and in particular the magnitude of J. By comparing the results on these compounds to the analogous MeOAn series, insights into design principles for creating improved spin-correlated radical pair systems for QIS studies are obtained.

Probing Bioinorganic Electron Spin Decoherence Mechanisms with an Fe2S2 Metalloprotein

Recent efforts have sought to develop paramagnetic molecular quantum bits (qubits) as a means to store and manipulate quantum information. Emerging structure-property relationships have shed light on electron spin decoherence mechanisms. While insights within molecular quantum information science have derived from synthetic systems, biomolecular platforms would allow for the study of decoherence phenomena in more complex chemical environments and further leverage molecular biology and protein engineering approaches. Here we have employed the exchange-coupled ST = 1/2 Fe2S2 active site of putidaredoxin, an electron transfer metalloprotein, as a platform for fundamental mechanistic studies of electron spin decoherence toward spin-based biological quantum sensing. At low temperatures, decoherence rates were anisotropic, reflecting a hyperfine-dominated decoherence mechanism, standing in contrast to the anisotropy of molecular systems observed previously. This mechanism provided a pathway for probing spatial effects on decoherence, such as protein vs solvent contributions. Furthermore, we demonstrated spatial sensitivity to single point mutations via site-directed mutagenesis and temporal sensitivity for monitoring solvent isotope exchange. Thus, this study demonstrates a step toward the design and construction of biomolecular quantum sensors.

A Paired-Ion Framework Composed of Vanadyl Porphyrin Molecular Qubits Extends Spin Coherence Times

Molecular electron spin qubits arranged in precise arrays have great potential for use in quantum information science applications. Molecular qubits are synthetically versatile and can be placed in ordered arrangements upon incorporation into a new class of materials known as paired-ion frameworks (PIFs). A PIF composed of vanadyl porphyrin molecular qubits, VOTCPP-PIF-1, was synthesized as single crystals. Electron paramagnetic resonance spectroscopy was used to study their spin coherence at temperatures up to 293 K. A suspension of VOTCPP-PIF-1 at 5 K in dimethylformamide (DMF) had a spin-spin relaxation time (Tm) of 270 ns. In DMF-d7 and at 5 K, the coherence time of this material increased to 370 ns. This increase in Tm is attributed to the lower gyromagnetic ratio of 2H compared to 1H, which results in weaker electron-nuclear dipolar coupling that reduces the effect of nuclear spin flips on electron spin coherence. In toluene, crystals of VOTCPP-PIF-1 had a Tm of 31 ns at 293 K, demonstrating that PIFs are a promising platform for creating materials for quantum information science applications.

Spin coherence and magnetization dynamics of TMA2[KCo1-xFex(CN)6] toward coordination-framework spin qubits

Metal compounds with S = 1/2 coordination-frameworks have been emerging as new powerful qubit candidates. In this study, we have reported the CN-based coordination framework TMA2[KCo1-xFex(CN)6] to be a qubit. We explored the magnetization dynamics and spin coherence of the magnetic dilution of the S = 1/2 Fe(III) complex TMA2[KFe(CN)6] (TMA = tetramethylammonium) in its Co(III)-based diamagnetic analogue TMA2[KCo(CN)6]. Alternating-current (AC) susceptibility data illustrate a slow magnetic relaxation upon applying a field of 0.1 T, which follows the phonon-bottleneck relaxation mechanism along with the Raman process. A magnetic relaxation time (τ) of 0.3 s (2% Fe) was realized at 1.8 K. Moreover, pulsed EPR data reveal a coherence duration of 1 μs (0.1% Fe) at 4 K with successful observation of Rabi oscillation at 4 K and 13 K (2% Fe) using MW pulses with variable irradiation-field strengths. The overall results indicate that TMA2[KCo1-xFex(CN)6] represents a promising qubit candidate, as it is capable of being placed in any superposition of the two distinct Ms states (Ms = +1/2 and Ms = -1/2).

Inductive detection of temperature-induced magnetization dynamics of molecular spin systems

The development and technological applications of molecular spin systems require versatile experimental techniques to characterize and control their static and dynamic magnetic properties. In the latter case, bulk spectroscopic and magnetometric techniques, such as AC magnetometry and pulsed electron paramagnetic resonance, are usually employed, showing high sensitivity, wide dynamic range, and flexibility. They are based on creating a nonequilibrium state either by changing the magnetic field or by applying resonant microwave radiation. Another possible source of perturbation is a laser pulse that rapidly heats the sample. This approach has proven to be one of the most useful techniques for studying the kinetics and mechanism of chemical and biochemical reactions. Inspired by these works, we propose an inductive detection of temperature-induced magnetization dynamics as applied to the study of molecular spin systems and describe the general design and construction of a particular induction probehead, taking into account the constraints imposed by the cryostat and electromagnet. To evaluate the performance, several coordination compounds of VO2+, Co2+, and Dy3+ were investigated using low-energy pulses of a terahertz free electron laser of the Novosibirsk free electron laser facility as a heat source. All measured magnetization dynamics were qualitatively or quantitatively described using a proposed basic theoretical model and compared with the data obtained by alternating current magnetometry. Based on the results of the research, the possible scope of applications of inductive detection and its advantages and disadvantages in comparison with standard methods are discussed.

An approach for patterned molecular adsorption on ferromagnets, achieved via Moiré superstructures

We have used a scanning tunneling microscope operated under ultrahigh vacuum conditions to investigate an oxo-vanadium-salen complex V(O)salen, that has potential applications as qubits in future quantum-based technologies. The adsorption and self-assembly of V(O)salen on a range of single crystal metal surfaces and nanoislands and the influence of substrate morphology and reactivity has been measured. On the close-packed flat Ag(111) and Cu(111) surfaces, the molecules adsorb isolated or form small clusters arranged randomly on the surface, whereas structured adsorption occurs on two types of Co nanoislands; Co grown on Ag(111) and Ag capped Co islands grown on Cu(111), both forming a Moiré pattern at the surface. The adsorption configuration can by scanning tunneling spectroscopy be linked to the geometric and electronic properties of the substrates and traced back to a Co d-related surface state, illustrating how the modulated reactivity can be used to engineer a pattern of adsorbed molecules on the nanoscale.

Dual Structure of a Vanadyl-Based Molecular Qubit Containing a Bis(β-diketonato) Ligand

We designed [VO(bdhb)] (1') as a new electronic qubit containing an oxovanadium(IV) ion (S = 1/2) embraced by a single bis(β-diketonato) ligand [H2bdhb = 1,3-bis(3,5-dioxo-1-hexyl)benzene]. The synthesis afforded three different crystal phases, all of which unexpectedly contain dimers with formula [(VO)2(bdhb)2] (1). A trigonal form (1h) with a honeycomb structure and 46% of solvent-accessible voids quantitatively transforms over time into a monoclinic solvatomorph 1m and minor amounts of a triclinic solventless phase (1a). In a static magnetic field, 1h and 1m have detectably slow magnetic relaxation at low temperatures through quantum tunneling and Raman mechanisms. Angle-resolved electron paramagnetic resonance (EPR) spectra on single crystals revealed signatures of low-dimensional magnetic behavior, which is solvatomorph-dependent, being the closest interdimer V···V separations (6.7-7.5 Å) much shorter than intramolecular V···V distances (11.9-12.1 Å). According to 1H diffusion ordered spectroscopy (DOSY) and EPR experiments, the complex adopts the desired monomeric structure in organic solution and its geometry was inferred from density functional theory (DFT) calculations. Spin relaxation measurements in a frozen toluene-d8/CD2Cl2 matrix yielded Tm values reaching 13 μs at 10 K, and coherent spin manipulations were demonstrated by Rabi nutation experiments at 70 K. The neutral quasi-macrocyclic structure, featuring nuclear spin-free donors and additional possibilities for chemical functionalization, makes 1' a new convenient spin-coherent building block in quantum technologies.

Oxovanadium electronics for in-memory, neuromorphic, and quantum computing applications

Vanadium is a critical raw material. In the nearby future, it may, however, become one of the key elements of computer devices based on two-dimensional arrays of spin qubits for quantum information processing or charge- and resistance-based data memory cells for non-volatile in-memory and neuromorphic computing. The research and development (R&D) of vanadium-containing electronic materials and methods for their responsible fabrication underpins the transition to innovative hybrid semiconductors for energy- and resource-efficient memory and information processing technologies. The combination of standard and emerging solid-state semiconductors with stimuli-responsive oxo complexes of vanadium(IV,V) is envisioned to result in electronics with a new room-temperature device nanophysics, and the ability to modulate and control it at the sub-nanometer level. The development of exponential (Boolean) logics based on the oxovanadium-comprising circuitry and crossbar arrays of individual memristive cells for in-memory computing, the implementation of basic synaptic functions via dynamic electrical pulses for neuromorphic computing, and the readout and control of spin networks and interfaces for quantum computing are strategically important future areas of molecular chemistry and applied physics of vanadium.

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.

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.

Numerically Exact Solution for a Real Polaritonic System under Vibrational Strong Coupling in Thermodynamic Equilibrium: Loss of Light-Matter Entanglement and Enhanced Fluctuations

The first numerically exact simulation of a full ab initio molecular quantum system (HD+) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled systems of mixed quantum statistics (bosons and Fermions) are discussed and circumvented by the specific choice of our molecular system. Our numerically exact simulations highlight the absence of zero temperature for the strongly coupled matter and light subsystems, due to cavity-induced noncanonical conditions. Furthermore, we explore the temperature dependency of light-matter quantum entanglement, which emerges for the ground state but is quickly lost already in the deep cryogenic regime. This is in contrast to predictions from the Jaynes-Cummings model, which is the standard starting point to model collective strong-coupling chemistry phenomenologically. Moreover, we find that the fluctuations of matter remain modified by the quantum nature of the thermal and vacuum-field fluctuations for significant temperatures, e.g., at ambient conditions. These observations (loss of entanglement and coupling to quantum fluctuations) have implications for the understanding and control of polaritonic chemistry and materials science, since a semiclassical theoretical description of light-matter interaction becomes reasonable, but the typical (classical) canonical equilibrium assumption for the nuclear subsystem remains violated. This opens the door for quantum fluctuation-induced stochastic resonance phenomena under vibrational strong coupling, which have been suggested as a plausible theoretical mechanism to explain the experimentally observed resonance phenomena in the absence of periodic driving that has not yet been fully understood.

Control and Transferability of Magnetic Interactions in Supramolecular Structures: Trimers of {Cr7 Ni} Antiferromagnetic Rings

A synthetic strategy is demonstrated to prepare two distinct trimers of antiferromagnetically coupled {Cr7 Ni} rings, substantially varying the magnetic interactions between the spin centres. The interactions were studied using multi-frequency cw EPR: in a trimer linked via non-covalent H-bonding interactions no measurable interaction between rings was seen, while in a trimer linked via iso-nicotinate groups isotropic and anisotropic exchange interactions of +0.42 and -0.8 GHz, respectively, were observed. The latter are the same as those for a simpler hetero-dimer system, showing how the spin-spin interactions can be built in a predictable and modular manner in these systems.

Coherences of Photoinduced Electron Spin Qubit Pair States in Photosystem I

This publication presents the first comprehensive experimental study of electron spin coherences in photosynthetic reaction center proteins, specifically focusing on photosystem I (PSI). The ultrafast electron transfer in PSI generates spin-correlated radical pairs (SCRPs), which are entangled spin pairs formed in well-defined spin states (Bell states). Since their discovery in our group in the 1980s, SCRPs have been extensively used to enhance our understanding of structure-function relationships in photosynthetic proteins. More recently, SCRPs have been utilized as tools for quantum sensing. Electron spin decoherence poses a significant challenge in realizing practical applications of electron spin qubits, particularly the creation of quantum entanglement between multiple electron spins. This work is focused on the systematic characterization of decoherence in SCRPs of PSI. These decoherence times were measured as electron spin echo decay times, termed phase memory times (TM), at various temperatures. Decoherence was recorded on both transient SCRP states P700+A1- and thermalized states. Our study reveals that TM exhibits minimal dependence on the biological species, biochemical treatment, and paramagnetic species. The analysis indicates that nuclear spin diffusion and instantaneous diffusion mechanisms alone cannot explain the observed decoherence. As a plausible explanation we discuss the assumption that the low-temperature dynamics of methyl groups in the protein surrounding the unpaired electron spin centers is the main factor governing the loss of the spin coherence in PSI.

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

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

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.

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.

Slow magnetic relaxation of a S = 1/2 copper(II)-substituted Keggin-type silicotungstate

This is the first report on slow magnetic relaxation in an S = 1/2 system based on a first-row transition metal ion with the polyoxometalate skeleton [(n-C₄H₉)₄N]₄H₂[SiW₁₁O₃₉Cu] (1). The X-band electron-spin-resonance spectrum of 1 measured at room temperature indicates that the copper ion experiences significantly reduced intermolecular interactions compared to the potassium salt and that it adopts a five-coordinated square-pyramidal coordination geometry. The AC magnetic-susceptibility measurements revealed that 1 undergoes slow magnetic relaxation in an applied static magnetic field (H_dc). The extracted spin-lattice relaxation time (92 ms at 1.8 K and H_dc = 5000 Oe) for 5% magnetically diluted 1, [(n-C₄H₉)₄N]₄H₂[SiW₁₁O₃₉Cu_0.05Zn_0.95] (dil.1), is comparable to those of other potential S = 1/2 spin qubits. A relaxation-time analysis indicated that Raman spin-lattice relaxation dominates even at low temperatures in an optimized field. The extracted Raman exponent (n = 2.30) is smaller than those of other S = 1/2 complexes that carry organic ligands, which implies that the decrease in relaxation time at higher temperatures is likely to be moderate.

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.

Towards Luminescent Vanadium(II) Complexes with Slow Magnetic Relaxation and Quantum Coherence

Molecular entities with doublet or triplet ground states find increasing interest as potential molecular quantum bits (qubits). Complexes with higher multiplicity might even function as qudits and serve to encode further quantum bits. Vanadium(II) ions in octahedral ligand fields with quartet ground states and small zero-field splittings qualify as qubits with optical read out thanks to potentially luminescent spin-flip states. We identified two V²⁺ complexes [V(ddpd)₂ ]²⁺ with the strong field ligand N,N'-dimethyl-N,N'-dipyridine-2-yl-pyridine-2,6-diamine (ddpd) in two isomeric forms (cis-fac and mer) as suitable candidates. The energy gaps between the two lowest Kramers doublets amount to 0.2 and 0.5 cm^-1 allowing pulsed EPR experiments at conventional Q-band frequencies (35 GHz). Both isomers possess spin-lattice relaxation times T₁ of around 300 μs and a phase memory time T_M of around 1 μs at 5 K. Furthermore, the mer isomer displays slow magnetic relaxation in an applied field of 400 mT. While the vanadium(III) complexes [V(ddpd)₂ ]³⁺ are emissive in the near-IR-II region, the [V(ddpd)₂ ]²⁺ complexes are non-luminescent due to metal-to-ligand charge transfer admixture to the spin-flip states.

Mixed-Sandwich Titanium(III) Qubits on Au(111): Electron Delocalization Ruled by Molecular Packing

Organometallic sandwich complexes are versatile molecular systems that have been recently employed for single-molecule manipulation and spin sensing experiments. Among related organometallic compounds, the mixed-sandwich S = 1/2 complex (η⁸-cyclooctatetraene)(η⁵-cyclopentadienyl)titanium, here [CpTi(cot)], has attracted interest as a spin qubit because of the long coherence time. Here the structural and chemical properties of [CpTi(cot)] on Au(111) are investigated at the monolayer level by experimental and computational methods. Scanning tunneling microscopy suggests that adsorption occurs in two molecular orientations, lying and standing, with a 3:1 ratio. XPS data evidence that a fraction of the molecules undergo partial electron transfer to gold, while our computational analysis suggests that only the standing molecules experience charge delocalization toward the surface. Such a phenomenon depends on intermolecular interactions that stabilize the molecular packing in the monolayer. This orientation-dependent molecule-surface hybridization opens exciting perspectives for selective control of the molecule-substrate spin delocalization in hybrid interfaces.

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.

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.

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.

Solid polymorphism and dynamic magnetic properties of a dodecylated vanadyl–porphyrinato complex: spin–lattice relaxations modulated by phase stabilisation

Phase stabilisation elongates spin–lattice relaxation times.

Tunable Cr4+ Molecular Color Centers

The inherent atomistic precision of synthetic chemistry enables bottom-up structural control over quantum bits, or qubits, for quantum technologies. Tuning paramagnetic molecular qubits that feature optical-spin initialization and readout is a crucial step toward designing bespoke qubits for applications in quantum sensing, networking, and computing. Here, we demonstrate that the electronic structure that enables optical-spin initialization and readout for S = 1, Cr(aryl)₄, where aryl = 2,4-dimethylphenyl (1), o-tolyl (2), and 2,3-dimethylphenyl (3), is readily translated into Cr(alkyl)₄ compounds, where alkyl = 2,2,2-triphenylethyl (4), (trimethylsilyl)methyl (5), and cyclohexyl (6). The small ground state zero field splitting values (<5 GHz) for 1-6 allowed for coherent spin manipulation at X-band microwave frequency, enabling temperature-, concentration-, and orientation-dependent investigations of the spin dynamics. Electronic absorption and emission spectroscopy confirmed the desired electronic structures for 4-6, which exhibit photoluminescence from 897 to 923 nm, while theoretical calculations elucidated the varied bonding interactions of the aryl and alkyl Cr⁴⁺ compounds. The combined experimental and theoretical comparison of Cr(aryl)₄ and Cr(alkyl)₄ systems illustrates the impact of the ligand field on both the ground state spin structure and excited state manifold, laying the groundwork for the design of structurally precise optically addressable molecular qubits.

Role of Coordination Geometry on the Magnetic Relaxation Dynamics of Isomeric Five-Coordinate Low-Spin Co(II) Complexes

To investigate the influence of the coordination geometry on the magnetization relaxation dynamics, two geometric isomers of a five-coordinate low-spin Co(II) complex with the general molecular formula [Co(DPPE)₂Cl]SnCl₃ (DPPE = diphenylphosphinoethane) were synthesized and structurally characterized. While one isomer has a square pyramidal geometry (Co-SP (1)), the other isomer figures a trigonal bipyramidal geometry (Co-TBP (2)). Both complexes were already reported elsewhere. The spin state of these complexes is unambiguously determined by detailed direct current (dc) magnetic data, X-band, and high-frequency EPR measurements. Slow relaxation of magnetization is commonly observed for systems with S > 1/2. However, both 1 and 2 show field-induced slow relaxation of magnetization. Especially 1 shows relaxation times up to τ = 35 ms at T = 1.8 K, which is much longer than the reported values for undiluted Co(II) low-spin monomers. In 2, the maximal field-induced relaxation time is suppressed to τ = 5 ms. We attribute this to the change in g-anisotropy, which is, in turn, correlated to the spatial arrangement of ligands (i.e., coordination geometry) around the Co(II) ions. Besides the detailed electronic structure of these complexes, the experimental observations are further corroborated by theoretical calculations.

Bis-Spiro-Oxetane and Bis-Spiro-Tetrahydrofuran Pyrroline Nitroxide Radicals: Synthesis and Electron Spin Relaxation Studies

Synthesis of bis-spiro-oxetane and bis-spiro-tetrahydrofuran pyrroline nitroxide radicals relies on the Mitsunobu reaction-mediated double cyclizations of N-Boc protected pyrroline tetraols. Structures of the nitroxide radicals are supported by X-ray crystallography. In a trehalose/sucrose matrix at room temperature, the bis-spiro-oxetane nitroxide radical possesses electron spin coherence time, Tm ≈ 0.7 μs. The observed enhanced Tm is most likely associated with strong hydrogen bonding of oxetane moieties to the trehalose/sucrose matrix.

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.

Binding Sites, Vibrations and Spin-Lattice Relaxation Times in Europium(II)-Based Metallofullerene Spin Qubits

To design molecular spin qubits with enhanced quantum coherence, a control of the coupling between the local vibrations and the spin states is crucial, which could be realized in principle by engineering molecular structures via coordination chemistry. To this end, understanding the underlying structural factors that govern the spin relaxation is a central topic. Here, we report the investigation of the spin dynamics in a series of chemically designed europium(II)-based endohedral metallofullerenes (EMFs). By introducing a unique structural difference, i. e. metal-cage binding site, while keeping other molecular parameters constant between different complexes, these manifest the key role of the three low-energy metal-displacing vibrations in mediating the spin-lattice relaxation times (T1 ). The temperature dependence of T1 can thus be normalized by the frequencies of these low energy vibrations to show an unprecedentedly universal behavior for EMFs in frozen CS2 solution. Our theoretical analysis indicates that this structural difference determines not only the vibrational rigidity but also spin-vibration coupling in these EMF-based qubit candidates.

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.

Assessing the Nature of Chiral-Induced Spin Selectivity by Magnetic Resonance

Understanding chiral-induced spin selectivity (CISS), resulting from charge transport through helical systems, has recently inspired many experimental and theoretical efforts but is still the object of intense debate. In order to assess the nature of CISS, we propose to focus on electron-transfer processes occurring at the single-molecule level. We design simple magnetic resonance experiments, exploiting a qubit as a highly sensitive and coherent magnetic sensor, to provide clear signatures of the acceptor polarization. Moreover, we show that information could even be obtained from time-resolved electron paramagnetic resonance experiments on a randomly oriented solution of molecules. The proposed experiments will unveil the role of chiral linkers in electron transfer and could also be exploited for quantum computing applications.

Deconvolving Contributions to Decoherence in Molecular Electron Spin Qubits: A Dynamic Ligand Field Approach

In the past decade, transition metal complexes have gained momentum as electron spin-based quantum bit (qubit) candidates due to their synthetic tunability and long achievable coherence times. The decoherence of magnetic quantum states imposes a limit on the use of these qubits for quantum information technologies, such as quantum computing, sensing, and communication. With rapid recent development in the field of molecular quantum information science, a variety of chemical design principles for prolonging coherence in molecular transition metal qubits have been proposed. Here the spin-spin, motional, and spin-phonon regimes of decoherence are delineated, outlining design principles for each. It is shown how dynamic ligand field models can provide insights into the intramolecular vibrational contributions in the spin-phonon decoherence regime. This minireview aims to inform the development of molecular quantum technologies tailored for different environments and conditions.