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.

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.

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.

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 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.

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.

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.

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.

A Cost-Effective Semi-Ab Initio Approach to Model Relaxation in Rare-Earth Single-Molecule Magnets.

We discuss a cost-effective approach to understand magnetic relaxation in the new generation of rare-earth single-molecule magnets. It combines ab initio calculations of the crystal field parameters, of the magneto-elastic coupling with local modes, and of the phonon density of states with fitting of only three microscopic parameters. Although much less demanding than a fully ab initio approach, the method gives important physical insights into the origin of the observed relaxation. By applying it to high-anisotropy compounds with very different relaxation, we demonstrate the power of the approach and pinpoint ingredients for improving the performance of single-molecule magnets.

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.

Targeting molecular quantum memory with embedded error correction.

The implementation of a quantum computer requires both to protect information from environmental noise and to implement quantum operations efficiently. Achieving this by a fully fault-tolerant platform, in which quantum gates are implemented within quantum-error corrected units, poses stringent requirements on the coherence and control of such hardware. A more feasible architecture could consist of connected memories, that support error-correction by enhancing coherence, and processing units, that ensure fast manipulations. We present here a supramolecular {Cr7Ni}-Cu system which could form the elementary unit of this platform, where the electronic spin 1/2 of {Cr7Ni} provides the processor and the naturally isolated nuclear spin 3/2 of the Cu ion is used to encode a logical unit with embedded quantum error-correction. We demonstrate by realistic simulations that microwave pulses allow us to rapidly implement gates on the processor and to swap information between the processor and the quantum memory. By combining the storage into the Cu nuclear spin with quantum error correction, information can be protected for times much longer than the processor coherence.

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.

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.

A heterometallic [LnLn'Ln] lanthanide complex as a qubit with embedded quantum error correction.

We show that a [Er-Ce-Er] molecular trinuclear coordination compound is a promising platform to implement the three-qubit quantum error correction code protecting against pure dephasing, the most important error in magnetic molecules. We characterize it by preparing the [Lu-Ce-Lu] and [Er-La-Er] analogues, which contain only one of the two types of qubit, and by combining magnetometry, low-temperature specific heat and electron paramagnetic resonance measurements on both the elementary constituents and the trimer. Using the resulting parameters, we demonstrate by numerical simulations that the proposed molecular device can efficiently suppress pure dephasing of the spin qubits.

Correction: Anisotropy of CoII transferred to the Cr7Co polymetallic cluster via strong exchange interactions.

[This corrects the article DOI: 10.1039/C8SC00163D.].

A two-qubit molecular architecture for electron-mediated nuclear quantum simulation.

A switchable interaction between pairs of highly coherent qubits is a crucial ingredient for the physical realization of quantum information processing. One promising route to enable quantum logic operations involves the use of nuclear spins as protected elementary units of information, qubits. Here we propose a simple way to use fast electronic spin excitations to switch the effective interaction between nuclear spin qubits and the realization of a two-qubit molecular architecture based on highly coherent vanadyl moieties to implement quantum logic operations. Controlled generation of entanglement between qubits is possible here through chemically tuned magnetic coupling between electronic spins, which is clearly evidenced by the splitting of the vanadium(iv) hyperfine lines in the continuous-wave electron paramagnetic resonance spectrum. The system has been further characterized by pulsed electron paramagnetic resonance spectroscopy, evidencing remarkably long coherence times. The experimentally derived spin Hamiltonian parameters have been used to simulate the system dynamics under the sequence of pulses required to implement quantum gates in a realistic description that includes also the harmful effect of decoherence. This demonstrates the possibility of using this molecular complex to implement a control-Z (CZ) gate and simple quantum simulations. Indeed, we also propose a proof-of-principle experiment based on the simulation of the quantum tunneling of the magnetization in a S = 1 spin system.

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.

Anisotropy of CoII transferred to the Cr7Co polymetallic cluster via strong exchange interactions.

The Cr7Co ring represents a model system to understand how the anisotropy of a CoII ion is transferred to the effective anisotropy of a polymetallic cluster by strong exchange interactions. Combining sizeable anisotropy with exchange interactions is an important point in the understanding and design of new anisotropic molecular nanomagnets addressing fundamental and applicative issues. By combining electron paramagnetic resonance and inelastic neutron scattering measurements with spin Hamiltonian and ab initio calculations, we have investigated in detail the anisotropy of the CoII ion embedded in the antiferromagnetic ring. Our results demonstrate a strong and anisotropic exchange interaction between the Co and the neighbouring Cr ions, which effectively transmits the anisotropy to the whole molecule.