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

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.

Synthesis and characterization of heterometallic rings templated through alkylammonium or imidazolium cations

We report the synthesis and structural characterization of a series of heterometallic rings templated via alkylammonium or imidazolium cations. The template and preference of each metal's coordination geometry can control the structure of heterometallic compounds, leading to octa-, nona-, deca-, dodeca-, and tetradeca-metallic rings. The compounds were characterized by single-crystal X-ray diffraction, elemental analysis, magnetometry, and EPR measurements. Magnetic measurements show that the exchange coupling between metal centres is antiferromagnetic. EPR spectroscopy shows that the spectra of {Cr7Zn} and {Cr9Zn} have S = 3/2 ground states, while the spectra of {Cr12Zn2} and {Cr8Zn} are consistent with S = 1 and 2 excited states. The EPR spectra of {(ImidH)-Cr6Zn2}, {(1-MeImH)-Cr8Zn2}, and {(1,2-diMeImH)-Cr8Zn2} include a combination of linkage isomers. The results on these related compounds allow us to examine the transferability of magnetic parameters between compounds.

Templating metallocycles with a macrocycle: synthesis, structures and magnetic studies of {Cr11M2} complexes

Addition of 1,4,8,11-tetrazacyclotetradecane (cyclam) to a reaction that produces octametallic rings when simpler amines are used, produces {Cr₁₁M₂} "pretzels" (M = Zn^II or Cu^II) where the cyclam coordinates to the M^II ion which then sits at the centre of a twelve-metal macrocycle. Magnetic studies were fitted using the finite-temperature Lanczos method (FTLM), and the results demonstrate that exchange interactions are transferable from previous exchange-coupled Cr^III rings.

A ferromagnetically coupled pseudo-calixarene [Co16] wheel that self-assembles as a tubular network of capsules

Reaction of Co(OAc)₂·4H₂O and Hsal in a basic MeCN solution affords the hexadecanuclear wheel [Co₁₆(sal)₁₆(OAc)₁₆]·16MeCN (1·16MeCN) that displays ferromagnetic nearest neighbour exchange and has pseudo-calixarene character. Symmetry equivalent wheels self-assemble to form remarkable tubular networks of capsules in the extended structure.

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.

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.

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.

Molecular Nanomagnets as Qubits with Embedded Quantum-Error Correction

We show that molecular nanomagnets have a potential advantage in the crucial rush toward quantum computers. Indeed, the sizable number of accessible low-energy states of these systems can be exploited to define qubits with embedded quantum error correction. We derive the scheme to achieve this crucial objective and the corresponding sequence of microwave/radiofrequency pulses needed for the error correction procedure. The effectiveness of our approach is shown already with a minimal S = 3/2 unit corresponding to an existing molecule, and the scaling to larger spin systems is quantitatively analyzed.

Molecular Nanomagnets as Qubits with Embedded Quantum-Error Correction

We show that molecular nanomagnets have a potential advantage in the crucial rush toward quantum computers. Indeed, the sizable number of accessible low-energy states of these systems can be exploited to define qubits with embedded quantum error correction. We derive the scheme to achieve this crucial objective and the corresponding sequence of microwave/radiofrequency pulses needed for the error correction procedure. The effectiveness of our approach is shown already with a minimal S = 3/2 unit corresponding to an existing molecule, and the scaling to larger spin systems is quantitatively analyzed.

Magnetic properties of transition metal dimers probed by inelastic neutron scattering

The physical characterisation and understanding of molecular magnetic materials is one of the most important steps towards the integration of such systems in hybrid spintronic devices. Amongst the many characterisation techniques employed in such a task, Inelastic Neutron Scattering (INS) stands as one of the most powerful and sensitive tools to investigate their spin dynamics. Herein, the magnetic properties and spin dynamics of two dinuclear complexes, namely [(M(hfacac)2)2(bpym)] (where M = Ni2+, Co2+, abbreviated in the following as Ni2, Co2) are reported. These are model systems that could constitute fundamental units of future spintronic devices. By exploiting the highly sensitive IN5 Cold INS spectrometer, we are able to gain a deep insight into the spin dynamics of Ni2 and to fully obtain the microscopic spin Hamiltonian parameters; while for Co2, a multitude of INS transitions are observed demonstrating the complexity of the magnetic properties of octahedral cobalt-based systems.

Homochiral hexanuclear nickel(ii) metallocyclic structures with high activity for the photocatalytic degradation of organic dyes

Two chiral hexanuclear nickel(ii) metallocyclic rings with new chiral ligands exhibit excellent activity for the photocatalytic degradation of organic dyes.

An Extensive Family of Heterometallic Titanium(IV)-Metal(III) Rings with Structure Control through Templates

A family of heterometallic [Cat][Ti_x MO_(x+1 )(O₂ C^t Bu)_2x+2 ] rings is reported where Cat=a secondary or tertiary alkyl ammonium ion, x=7, 8 or 9, and M=Fe^III , Ga^III , Cr^III , In^III and Al^III . The structures are regular polygons with eight, nine or ten vertices with each edge bridged by an oxide and two pivalates. The size of the ring formed is controlled by the alkylammonium cation present. In each case a homometallic by-product is found [Cat][Ti_x O_(x+1 )(O₂ C^t Bu)_2x-1 ].

[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) ).

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 Cr₈Mn, a nine‐membered antiferromagnetic (AF) molecular nanomagnet, are investigated. Cr₈Mn 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 Cr₈Mn 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 Cr₈Mn. 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.