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.

Chiral-induced spin selectivity in photo-induced electron transfer: Investigating charge and spin dynamics in a master equation framework.

Investigating the role of chiral-induced spin selectivity in the generation of spin correlated radical pairs in a photoexcited donor-chiral bridge-acceptor system is fundamental to exploit it in quantum technologies. This requires a minimal master equation description of both charge separation and recombination through a chiral bridge. To achieve this without adding complexity and entering in the microscopic origin of the phenomenon, we investigate the implications of spin-polarizing reaction operators to the master equation. The explicit inclusion of coherent evolution yields non-trivial behaviors in the charge and spin dynamics of the system. Finally, we apply this master equation to a setup comprising a molecular qubit attached to the donor-bridge-acceptor molecule, enabling qubit initialization, control, and read-out. Promising results are found by simulating this sequence of operations assuming realistic parameters and achievable experimental conditions.

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.

Correction: Quantum error correction with molecular spin qudits.

Correction for 'Quantum error correction with molecular spin qudits' by Mario Chizzini et al., Phys. Chem. Chem. Phys., 2022, https://doi.org/10.1039/D2CP01228F.

Quantum error correction with molecular spin qudits.

Thanks to the large number of levels which can be coherently manipulated, molecular spin systems constitute a very promising platform for quantum computing. Indeed, they can embed quantum error correction within single molecular objects, thus greatly simplifying its actual realization in the short term. We consider a recent proposal, which exploits a spin qudit to encode the protected unit, and is tailored to fight pure dephasing. Here we compare the implementation of this code on different molecules, in which the qudit is provided by either an electronic or a nuclear spin (S, I > 1), coupled to a spin-1/2 electronic ancilla for error detection. By thorough numerical simulations we show that a significant gain in the effective phase memory time can be achieved. This is further enhanced by exploiting pulse-shaping techniques to reduce the leakage and/or the impact of decoherence during correction. Moreover, we simulate the implementation of single-qubit operations on the encoded states.

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; 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.

Quantum Simulation of Three-Body Interactions in Weakly Driven Quantum Systems.

The realization of effective Hamiltonians featuring many-body interactions beyond pairwise coupling would enable the quantum simulation of central models underpinning topological physics and quantum computation. We overcome crucial limitations of perturbative Floquet engineering and discuss the highly accurate realization of a purely three-body Hamiltonian in superconducting circuits and molecular nanomagnets.

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.

Slow Magnetic Relaxation of a 12-Metallacrown-4 Complex with a Manganese(III)-Copper(II) Heterometallic Ring Motif.

The heterobimetallic metallacrown (MC), (TMA)2{Mn(OAc)2[12-MCMn(III)Cu(II)N(shi)-4](CH3OH)}·2.90CH3OH, 1, where TMA+ is tetramethylammonium, -OAc is acetate, and shi3- is salicylhydroximate, consists of a MnII ion captured in the central cavity and alternating unambiguous and ordered manganese(III) and copper(II) sites about the MC ring, a first for the archetypal MC structure design. DC-magnetometry characterization and subsequent simulation with the Spin Hamiltonian H = -J1(s1 + s3)·s5 - J2(s2 + s4)·s5 - J3Σi=14si·si+1 + d(sz,12 + sz,32) + µBΣj=15gjsj·B indicates an S = 5/2 ground state and a sizable axial zero-field splitting on MnIII. AC-susceptibility measurements reveal that 1 displays slow magnetization relaxation akin to single-molecule magnet (SMM) behavior.

Coherent Manipulation of a Molecular Ln-Based Nuclear Qudit Coupled to an Electron Qubit.

We demonstrate that the [Yb(trensal)] molecule is a prototypical coupled electronic qubit-nuclear qudit system. The combination of noise-resilient nuclear degrees of freedom and large reduction of nutation time induced by electron-nuclear mixing enables coherent manipulation of this qudit by radio frequency pulses. Moreover, the multilevel structure of the qudit is exploited to encode and operate a qubit with embedded basic quantum error correction.

Measurement of Magnetic Exchange in Asymmetric Lanthanide Dimetallics: Toward a Transferable Theoretical Framework.

Magnetic exchange interactions within the asymmetric dimetallic compounds [hqH2][Ln2(hq)4(NO3)3]·MeOH, (Ln = Er(III) and Yb(III), hqH = 8-hydroxyquinoline) have been directly probed with EPR spectroscopy and accurately modeled by spin Hamiltonian techniques. Exploitation of site selectivity via doping experiments in Y(III) and Lu(III) matrices yields simple EPR spectra corresponding to isolated Kramers doublets, allowing determination of the local magnetic properties of the individual sites within the dimetallic compounds. CASSCF-SO calculations and INS and far-IR measurements are all employed to further support the identification and modeling of the local electronic structure for each site. EPR spectra of the pure dimetallic compounds are highly featured and correspond to transitions within the lowest-lying exchange-coupled manifold, permitting determination of the highly anisotropic magnetic exchange between the lanthanide ions. We find a unique orientation for the exchange interaction, corresponding to a common elongated oxygen bridge for both isostructural analogs. This suggests a microscopic physical connection to the magnetic superexchange. These results are of fundamental importance for building and validating model microscopic Hamiltonians to understand the origins of magnetic interactions between lanthanides and how they may be controlled with chemistry.

Studies of a Large Odd-Numbered Odd-Electron Metal Ring: Inelastic Neutron Scattering and Muon Spin Relaxation Spectroscopy of Cr8 Mn.

The spin dynamics of Cr8 Mn, a nine-membered antiferromagnetic (AF) molecular nanomagnet, are investigated. Cr8 Mn is a rare example of a large odd-membered AF ring, and has an odd-number of 3d-electrons present. Odd-membered AF rings are unusual and of interest due to the presence of competing exchange interactions that result in frustrated-spin ground states. The chemical synthesis and structures of two Cr8 Mn variants that differ only in their crystal packing are reported. Evidence of spin frustration is investigated by inelastic neutron scattering (INS) and muon spin relaxation spectroscopy (µSR). From INS studies we accurately determine an appropriate microscopic spin Hamiltonian and we show that µSR is sensitive to the ground-spin-state crossing from S=1/2 to S=3/2 in Cr8 Mn. The estimated width of the muon asymmetry resonance is consistent with the presence of an avoided crossing. The investigation of the internal spin structure of the ground state, through the analysis of spin-pair correlations and scalar-spin chirality, shows a non-collinear spin structure that fluctuates between non-planar states of opposite chiralities.

[CrF(O2 C(t) Bu)2 ]9 : Synthesis and Characterization of a Regular Homometallic Ring with an Odd Number of Metal Centers and Electrons.

The first regular homometallic ring containing an odd number of metal centers is reported. The ring was synthesized by means of amine-templated self-assembly. Extensive physical characterization studies, including magnetic measurements, powder inelastic neutron scattering (INS), and DFT calculations, show that the molecule has a near perfect match to the expected behavior for a frustrated system with the lowest energy pair of S=1/2 spin states separated by only 0.1 meV (0.8 cm(-1) ).

Low temperature magnetic properties and spin dynamics in single crystals of Cr8Zn antiferromagnetic molecular rings.

A detailed experimental investigation of the effects giving rise to the magnetic energy level structure in the vicinity of the level crossing (LC) at low temperature is reported for the open antiferromagnetic molecular ring Cr8Zn. The study is conducted by means of thermodynamic techniques (torque magnetometry, magnetization and specific heat measurements) and microscopic techniques (nuclear magnetic resonance line width, nuclear spin lattice, and spin-spin relaxation measurements). The experimental results are shown to be in excellent agreement with theoretical calculations based on a minimal spin model Hamiltonian, which includes a Dzyaloshinskii-Moriya interaction. The first ground state level crossing at µ0Hc1 = 2.15 T is found to be an almost true LC while the second LC at µ0Hc2 = 6.95 T has an anti-crossing gap of Δ12 = 0.19 K. In addition, both NMR and specific heat measurements show the presence of a level anti-crossing between excited states at µ0H = 4.5 T as predicted by the theory. In all cases, the fit of the experimental data is improved by introducing a distribution of the isotropic exchange couplings (J), i.e., using a J strain model. The peaks at the first and second LCs in the nuclear spin-lattice relaxation rate are dominated by inelastic scattering and a value of Γ âˆ¼ 10(10) rad/s is inferred for the life time broadening of the excited state of the open ring, due to spin phonon interaction. A loss of NMR signal (wipe-out effect) is observed for the first time at LC and is explained by the enhancement of the spin-spin relaxation rate due to the inelastic scattering.

A detailed study of the magnetism of chiral {Cr7M} rings: an investigation into parametrization and transferability of parameters.

Compounds of general formula [Cr7MF3(Etglu)(O2C(t)Bu)15(Phpy)] [H5Etglu = N-ethyl-d-glucamine; Phpy = 4-phenylpyridine; M = Zn (1), Mn (2), Ni (3)] have been prepared. The structures contain an irregular octagon of metal sites formed around the penta-deprotonated Etglu(5-) ligand; the chirality of N-ethyl-d-glucamine is retained in the final product. The seven Cr(III) sites have a range of coordination environments, and the divalent metal site is crystallographically identified and has a Phpy ligand attached to it. By using complementary experimental techniques, including magnetization and specific heat measurements, inelastic neutron scattering, and electron paramagnetic resonance spectroscopy, we have investigated the magnetic features of this family of {Cr7M} rings. Microscopic parameters of the spin Hamiltonian have been determined as a result of best fits of the different experimental data, allowing a direct comparison with corresponding parameters found in the parent compounds. We examine whether these parameters can be transferred between compounds and compare them with those of an earlier family of heterometallic rings.

Chirality-Induced Spin Selectivity: An Enabling Technology for Quantum Applications.

Molecular spins are promising building blocks of future quantum technologies thanks to the unparalleled flexibility provided by chemistry, which allows the design of complex structures targeted for specific applications. However, their weak interaction with external stimuli makes it difficult to access their state at the single-molecule level, a fundamental tool for their use, for example, in quantum computing and sensing. Here, an innovative solution exploiting the interplay between chirality and magnetism using the chirality-induced spin selectivity effect on electron transfer processes is foreseen. It is envisioned to use a spin-to-charge conversion mechanism that can be realized by connecting a molecular spin qubit to a dyad where an electron donor and an electron acceptor are linked by a chiral bridge. By numerical simulations based on realistic parameters, it is shown that the chirality-induced spin selectivity effect could enable initialization, manipulation, and single-spin readout of molecular qubits and qudits even at relatively high temperatures.

Direct observation of chirality-induced spin selectivity in electron donor-acceptor molecules.

The role of chirality in determining the spin dynamics of photoinduced electron transfer in donor-acceptor molecules remains an open question. Although chirality-induced spin selectivity (CISS) has been demonstrated in molecules bound to substrates, experimental information about whether this process influences spin dynamics in the molecules themselves is lacking. Here we used time-resolved electron paramagnetic resonance spectroscopy to show that CISS strongly influences the spin dynamics of isolated covalent donor-chiral bridge-acceptor (D-Bχ-A) molecules in which selective photoexcitation of D is followed by two rapid, sequential electron-transfer events to yield D•+-Bχ-A•-. Exploiting this phenomenon affords the possibility of using chiral molecular building blocks to control electron spin states in quantum information applications.

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.

Chemical control of spin propagation between heterometallic rings.

We present a synthetic, structural, theoretical, and spectroscopic study of a family of heterometallic ring dimers which have the formula [{Cr(7)NiF(3)(Etglu)(O(2)CtBu)(15)}(2)(NLN)], in which Etglu is the pentadeprotonated form of the sugar N-ethyl-D-glucamine, and NLN is an aromatic bridging diimine ligand. By varying NLN we are able to adjust the strength of the interaction between rings with the aim of understanding how to tune our system to achieve weak magnetic communication between the spins, a prerequisite for quantum entanglement. Micro-SQUID and EPR data reveal that the magnetic coupling between rings is partly related to the through-bond distance between the spin centers, but also depends on spin-polarization mechanisms and torsion angles between aromatic rings. Density functional theory (DFT) calculations allow us to make predictions of how such chemically variable parameters could be used to tune very precisely the interaction in such systems. For possible applications in quantum information processing and molecular spintronics, such precise control is essential.

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.