Molecular Qubits Research Articles

Coherence in Chemistry: Foundations and Frontiers.

Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.

Toward Quantum Noses: Quantum Chemosensing Based on Molecular Qubits in Metal-Organic Frameworks.

ConspectusQuantum sensing leverages quantum properties to enhance the sensitivity and resolution of sensors beyond their classical sensing limits. Quantum sensors, such as diamond defect centers, have been developed to detect various physical properties, including magnetic fields and temperature. However, the spins of defects are buried within dense solids, making it difficult for them to strongly interact with molecular analytes. Therefore, nanoporous materials have been implemented in combination with electron spin center of molecules (molecular qubits) to produce quantum chemosensors that can distinguish various chemical substances. Molecular qubits have a uniform structure, and their properties can be precisely controlled by changing their chemical structure. Metal-organic frameworks (MOFs) are suitable for supporting molecular qubits because of their high porosity, structural regularity, and designability. Molecular qubits can be inserted in the MOF structures or adsorbed as guest molecules. The qubits in the MOF can interact with analytes upon exposure, providing an effective and tunable sensing platform.In this Account, we review the recent progress in qubit-MOF hybrids toward the realization of room-temperature quantum chemosensing. Molecular qubits can be introduced in controlled concentrations at targeted positions by exploiting metal ions, ligands, or guests that compose the MOF. Heavy metal-free organic chromophores have several outstanding features as molecular qubits; namely, they can be initialized by light irradiation and exhibit relatively long coherence times of submicroseconds to microseconds, even at room temperature. One detection method involves monitoring the hyperfine interaction between the electron spins of the molecular qubits and the nuclear spins of the analyte incorporated in the pore. There is also an indirect detection method that relies on the motional change in molecular qubits. If the motion of the molecular qubit changes with the adsorption of the analyte, it can be detected as a change in the spin relaxation process. This mechanism is unique to qubits exposed in nanopores, not observed in conventional qubits embedded in dense solids.By maximizing the guest recognition ability of MOFs and the environmental sensitivity of qubits, quantum chemosensing that recognizes specific chemical species in a highly selective and sensitive manner may be possible. It is difficult to distinguish between diverse chemical species by employing only one combination of MOF and qubit, but by creating arrays of different qubit-MOF hybrids, it would become possible to distinguish between various analytes based on pattern recognition. Inspired by the human olfactory mechanism, we propose the use of multiple qubit-MOF hybrids and pattern recognition to identify specific molecules. This system represents a quantum version of olfaction, and thus we propose the concept of a "quantum nose." Quantum noses may be used to recognize biometabolites and biomarkers and enable new medical diagnostic technologies and olfactory digitization.

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.

Luminescent Organic Triplet Diradicals as Optically Addressable Molecular Qubits.

Optical-spin interfaces that enable the photoinitialization, coherent microwave manipulation, and optical read-out of ground state spins have been studied extensively in solid-state defects such as diamond nitrogen vacancy (NV) centers and are promising for quantum information science applications. Molecular quantum bits (qubits) offer many advantages over solid-state spin centers through synthetic control of their optical and spin properties and their scalability into well-defined multiqubit arrays. In this work, we report an optical-spin interface in an organic molecular qubit consisting of two luminescent tris(2,4,6-trichlorophenyl)methyl (TTM) radicals connected via the meta-positions of a phenyl linker. The triplet ground state of this system can be photoinitialized in its |T0⟩ state by shelving triplet populations as singlets through spin-selective excited-state intersystem crossing with 80% selectivity from |T+⟩ and |T-⟩. The fluorescence intensity in the triplet manifold is determined by the ground-state polarization, and we show successful optical read-out of the ground-state spin following microwave manipulations by fluorescence-detected magnetic resonance spectroscopy. At 85 K, the lifetime of the polarized ground state is 45 ± 3 μs, and the ground state phase memory time is Tm = 5.9 ± 0.1 μs, which increases to 26.8 ± 1.6 μs at 5 K. These results show that luminescent diradicals with triplet ground states can serve as optically addressable molecular qubits with long spin coherence times, which marks an important step toward the rational design of spin-optical interfaces in organic materials.

Macrocyclic Parallel Dimer Showing Quantum Coherence of Quintet Multiexcitons at Room Temperature.

Singlet fission (SF) is a promising approach in quantum information science because it can generate spin-entangled quintet triplet pairs by photoexcitation independent of temperature. However, it is still challenging to rationally achieve quantum coherence at room temperature, which requires precise control of the orientation and dynamics of triplet pairs. Here we show that the quantum coherence of quintet multiexcitons can be achieved at room temperature by arranging two pentacene chromophores in parallel and in close proximity within a macrocycle. By making dynamic covalent Schiff-base bonds between aldehyde-modified pentacene derivatives, macrocyclic parallel dimer-1 (MPD-1) can be selectively synthesized in a high yield. MPD-1 exhibits fast subpicosecond SF in polystyrene film and generates spin-polarized quintet multiexcitons. Furthermore, the coherence time T2 of the MPD-1 quintet is as long as 648 ns, even at room temperature. This macrocyclic parallel dimer strategy opens up new possibilities for future quantum applications using molecular multilevel qubits.

CaY@C2n: Exploring Molecular Qubits with Ca-Y Metal-Metal Bonds.

Metal-metal bonding is crucial in chemistry for advancing our understanding of the fundamental aspects of chemical bonds. Metal-metal bonds based on alkaline-earth (Ae) elements, especially the heavier Ae elements (Ca, Sr, and Ba), are rarely reported due to their high electropositivity. Herein, we report two heteronuclear di-EMFs CaY@Cs(6)-C82 and CaY@C2v(5)-C80, which contain unprecedented single-electron Ca-Y metal-metal bonds. These compounds were characterized by single-crystal X-ray crystallography, electron paramagnetic resonance (EPR) spectroscopy, and DFT calculations. The crystallographic study of CaY@Cs(6)-C82 shows that Ca and Y are successfully encapsulated into the carbon cage with a Ca-Y distance of 3.691 Å. The CW-EPR study of both CaY@Cs(6)-C82 and CaY@C2v(5)-C80 exhibits a doublet, suggesting the presence of an unpaired electron located between Ca and Y. The combined experimental and theoretical results confirm the presence of a Ca-Y single-electron metal-metal bond with substantial covalent interaction, attributed to significant overlap between the 4s4p orbitals of Ca and the 5s5p4d orbitals of Y. Furthermore, pulse EPR spectroscopy was used to investigate the quantum coherence of the electron spin within this bond. The unpaired electron, characterized by its s orbital nature, is effectively protected by the carbon cage, resulting in efficient suppression of both spin-lattice relaxation and decoherence. CaY@Cs(6)-C82 behaves as an electron spin qubit, displaying a maximum decoherence time of 7.74 μs at 40 K. This study reveals an unprecedented Ae-rare-earth metal-metal bond stabilized by the fullerene cages and elucidates the molecular qubit properties stemming from their unique bonding character, highlighting their potential in quantum information processing applications.

Modulation of triplet quantum coherence by guest-induced structural changes in a flexible metal-organic framework

Quantum sensing has the potential to improve the sensitivity of chemical sensing by exploiting the characteristics of qubits, which are sensitive to the external environment. Modulation of quantum coherence by target analytes can be a useful tool for quantum sensing. Using molecular qubits is expected to provide excellent sensitivity due to the proximity of the sensor to the target analyte. However, many molecular qubits are used at cryogenic temperatures, and how to make molecular qubits respond to specific analytes remains unclear. Here, we propose a material design in which the coherence time changes in response to a variety of analytes at room temperature. We used the photoexcited triplet, which can be initialized at room temperature, as qubits and introduce them to a metal–organic framework that can flexibly change its pore structure in response to guest adsorption. By changing the local molecular density around the triplet qubits by adsorption of a specific analyte, the mobility of the triplet qubit can be changed, and the coherence time can be made responsive.

(η8-Cyclooctatetraene)(η5-fluorenyl)titanium: a processable molecular spin qubit with optimized control of the molecule-substrate interface.

Depositing single paramagnetic molecules on surfaces for sensing and quantum computing applications requires subtle topological control. To overcome issues that are often encountered with sandwich metal complexes, we exploit here the low symmetry architecture and suitable vaporability of mixed-sandwich [FluTi(cot)], Flu = fluorenyl, cot = cyclooctatetraene, to drive submonolayer coverage and select an adsorption configuration that preserves the spin of molecules deposited on Au(111). Electron paramagnetic resonance spectroscopy and ab initio quantum computation evidence a d z 2 ground state that protects the spin from phonon-induced relaxation. Additionally, computed and measured spin coherence times exceed 10 μs despite the molecules being rich in hydrogen. A thorough submonolayer investigation by scanning tunneling microscopy, X-ray photoelectron and absorption spectrocopies and X-ray magnetic circular dichroism measurements supported by DFT calculations reveals that the most stable configuration, with the fluorenyl in contact with the metal surface, prevents titanium(iii) oxidation and spin delocalization to the surface. This is a necessary condition for single molecular spin qubit addressing on surfaces.

Calculation of π Using a Molecular Electron Spin Qubit Implemented by Pulsed Electron Paramagnetic Resonance.

The present letter demonstrates a simple method to characterize the molecular electron spin qubits, for which a large number of chemical compounds with non-zero spin have been proposed. The method is based on calculating the value of π using a one-qubit protocol based on obtaining and processing Rabi oscillations. It was implemented using a model system of a Finland trityl radical with an electron spin S = 1/2 and a pulsed electron paramagnetic resonance spectrometer. As a result, the value of π was obtained with an accuracy of two decimal places, and an analysis of statistical and systematic errors was carried out.

Coherent Addressing of Single Molecular Electron Spin Qubits

AbstractWith rational designability, versatile tunability, and quantum coherence, molecular electron spin qubits could offer new opportunities for quantum information science, enabling simplified implementation of quantum algorithms and chemical‐specific quantum sensing. The development of these transformative technologies relies on coherent addressing of single molecular electron spin qubits with high initialization, manipulation, and readout fidelities. This is unfeasible to conventional electron spin resonance spectroscopy, which is widely used for coherent addressing of ensemble electron spins, due to its low initialization efficiency and readout sensitivity. Taking advantage of single spin detectability of single‐molecule spectroscopy, scanning tunneling microscopy, atomic force microscopy, and quantum metrology, several strategies have been developed to empower electron spin resonance spectroscopy with single qubit addressability. In this Emerging Topic, we introduce principles and technical implementation of strategies for coherent addressing of single molecular electron spin qubits, discuss their potential applicability in quantum technologies, and point out their challenges in terms of scalability, molecular design, and/or decoherence suppression. We discuss future directions to overcome these challenges and to improve single qubit addressing technologies, which will facilitate the advancement of molecular quantum information science.

Detrimental Increase of Spin-Phonon Coupling in Molecular Qubits on Substrates.

Molecular qubits are a promising platform for quantum information systems. Although single molecule and ensemble studies have assessed the performance of S = 1/2 molecules, it is understood that to function in devices, regular arrays of addressable qubits supported by a substrate are needed. The substrate imposes mechanical and electronic boundary conditions on the molecule; however, the impact of these effects on spin-lattice relaxation times is not well understood. Here we perform electronic structure calculations to assess the effects of a graphene (Cgr) substrate on the molecular qubit copper phthalocyanine (CuPc). We use a progressive Hessian approach to efficiently calculate and separate the substrate contributions. We also use a simple thermal model to predict the impact of these changes on the spin-phonon coupling from 0 to 200 K. Further analysis of the individual vibrational modes with and without Cgr shows that an overall increase in SPC between the vibrations modes of CuPc with the surface reduces the spin-lattice relaxation time T1. We explain these changes by examining how the substrate lifts symmetries of CuPc in the absorbed configuration. Our work shows that a surface can have a large unintentional impact on SPC and that ways to reduce this coupling need to be found to fully exploit arrays of molecular qubits in device architectures.

Spin-lattice relaxation with non-linear couplings: Comparison between Fermi's golden rule and extended dissipaton equation of motion.

Fermi's golden rule (FGR) offers an empirical framework for understanding the dynamics of spin-lattice relaxation in magnetic molecules, encompassing mechanisms like direct (one-phonon) and Raman (two-phonon) processes. These principles effectively model experimental longitudinal relaxation rates, denoted as T1-1. However, under scenarios of increased coupling strength and nonlinear spin-lattice interactions, FGR's applicability may diminish. This paper numerically evaluates the exact spin-lattice relaxation rate kernels, employing the extended dissipaton equation of motion formalism. Our calculations reveal that when quadratic spin-lattice coupling is considered, the rate kernels exhibit a free induction decay-like feature, and the damping rates depend on the interaction strength. We observe that the temperature dependence predicted by FGR significantly deviates from the exact results since FGR ignores the higher order effects and the non-Markovian nature of spin-lattice relaxation. Our methods can be easily extended to study other systems with nonlinear spin-lattice interactions and provide valuable insights into the temperature dependence of T1 in molecular qubits when the coupling is strong.

Spin-Lattice Relaxation and Spin-Phonon Coupling of ns1 Metal Ions at the Surface.

To use transition metal ions for spin-based applications, it is essential to understand fundamental contributions to electron spin relaxation in different ligand environments. For example, to serve as building blocks for a device, transition metal ion-based molecular qubits must be organized on surfaces and preserve long electron spin relaxation times, up to room temperature. Here we propose monovalent group 12 ions (Zn+ and Cd+) as potential electronic metal qubits with an ns1 ground state. The relaxation properties of Zn+ and Cd+, stabilized at the interface of porous aluminosilicates, are investigated and benchmarked against vanadium (3d1) and copper (3d9) ions. The spin-phonon coupling has been evaluated through DFT modeling and found to be negligible for the ns1 states, explaining the long coherence time, up to 2 μs, at room temperature. These so far unexplored metal qubits may represent viable candidates for room temperature quantum operations and sensing.

Blue-Detuned Magneto-optical Trap of CaF Molecules.

A key method to produce trapped and laser-cooled molecules is the magneto-optical trap (MOT), which is conventionally created using light red detuned from an optical transition. In this work, we report a MOT for CaF molecules created using blue-detuned light. The blue-detuned MOT (BDM) achieves temperatures well below the Doppler limit and provides the highest densities and phase-space densities reported to date in CaF MOTs. Our results suggest that BDMs are likely achievable in many relatively light molecules including polyatomic ones, but our measurements suggest that BDMs will be challenging to realize in substantially heavier molecules due to sub-mK trap depths. In addition to record temperatures and densities, we find that the BDM substantially simplifies and enhances the loading of molecules into optical tweezer arrays, which are a promising platform for quantum simulation and quantum information processing. Notably, the BDM reduces molecular number requirements ninefold compared to a conventional red-detuned MOT, while not requiring additional hardware. Our work therefore substantially simplifies preparing large-scale molecular tweezer arrays, which are a novel platform for simulation of quantum many-body dynamics and quantum information processing with molecular qubits.

Quantifying the effects of peripheral substituents on the spin-lattice relaxation of a vanadyl molecular quantum bit

Electron spin superpositions represent a critical component of emergent quantum technologies in computation, sensing, encryption, and communication. However, spin relaxation (T1) and decoherence (Tm) represent major obstacles to the implementation of molecular quantum bits (qubits). Synthetic strategies have made substantial progress in enhancing spin coherence times by minimizing contributions from surrounding electron and nuclear spins. For room-temperature operation, however, the lifetime of spin coherence becomes limited by coupling with vibrational modes of the lattice. Using pulse electron paramagnetic resonance (EPR) spectroscopy, we measure the spin-lattice relaxation of a vanadyl tetrapyrazinoporphyrazine complex appended with eight peripheral 2,6-diisopropylphenol groups (VOPyzPz-DIPP) and compare it to the relaxation of the archetypical vanadyl phthalocyanine molecular qubit (VOPc). The added peripheral groups lead to distinctly different spin relaxation behavior. While similar relaxation times are observed at low temperatures and ambient conditions, significant changes are observed for the orientation dependence of T1 at 100 K, as well as the temperature dependence of T1 over the intermediate temperature range spanning [Formula: see text]10–150 K. These results can be tentatively interpreted as arising from loosened spin-phonon coupling selection rules and a greater number of accessible acoustic and optical modes contributing to the spin relaxation behavior of VOPyzPz-DIPP relative to VOPc.

Alternant Hydrocarbon Diradicals as Optically Addressable Molecular Qubits.

High-spin molecules allow for bottom-up qubit design and are promising platforms for magnetic sensing and quantum information science. Optical addressability of molecular electron spins has also been proposed in first-row transition-metal complexes via optically detected magnetic resonance (ODMR) mechanisms analogous to the diamond-nitrogen-vacancy color center. However, significantly less progress has been made on the front of metal-free molecules, which can deliver lower costs and milder environmental impacts. At present, most luminescent open-shell organic molecules are π-diradicals, but such systems often suffer from poor ground-state open-shell characters necessary to realize a stable ground-state molecular qubit. In this work, we use alternancy symmetry to selectively minimize radical-radical interactions in the ground state, generating π-systems with high diradical characters. We call them m-dimers, referencing the need to covalently link two benzylic radicals at their meta carbon atoms for the desired symmetry. Through a detailed electronic structure analysis, we find that the excited states of alternant hydrocarbon m-diradicals contain important symmetries that can be used to construct ODMR mechanisms leading to ground-state spin polarization. The molecular parameters are set in the context of a tris(2,4,6-trichlorophenyl)methyl (TTM) radical dimer covalently tethered at the meta position, demonstrating the feasibility of alternant m-diradicals as molecular color centers.

Metalloporphyrins as Building Blocks for Quantum Information Science

AbstractThe intrinsic quantum nature of molecules opens exciting opportunities for developing the field of quantum information science. In this context, porphyrins stand out as ideal building blocks for quantum technologies thanks to their unique optical and electrical properties as well as their capacity to accommodate metal atoms and ions. This review bridges the chemistry and physics of porphyrins, providing an overview of recent advances in porphyrin‐based molecular qubits. Starting from qubits, the review explores the potential of porphyrin units to combine, leading to the formation of quantum logic gates and hierarchical higher‐dimensional structures. Next, the exploitation of porphyrins' unique photophysical properties for realizing long‐lived high spin states is examined. These states are promising for the photogeneration of multi‐level systems and the optical initialization and control of molecular qubits. With a critical eye on the current state‐of‐the‐art, the review elucidates the future perspectives of porphyrins for advancing quantum technologies.

Optical Phenomena in Molecule-Based Magnetic Materials.

Since the last century, we have witnessed the development of molecular magnetism which deals with magnetic materials based on molecular species, i.e., organic radicals and metal complexes. Among them, the broadest attention was devoted to molecule-based ferro-/ferrimagnets, spin transition materials, including those exploring electron transfer, molecular nanomagnets, such as single-molecule magnets (SMMs), molecular qubits, and stimuli-responsive magnetic materials. Their physical properties open the application horizons in sensors, data storage, spintronics, and quantum computation. It was found that various optical phenomena, such as thermochromism, photoswitching of magnetic and optical characteristics, luminescence, nonlinear optical and chiroptical effects, as well as optical responsivity to external stimuli, can be implemented into molecule-based magnetic materials. Moreover, the fruitful interactions of these optical effects with magnetism in molecule-based materials can provide new physical cross-effects and multifunctionality, enriching the applications in optical, electronic, and magnetic devices. This Review aims to show the scope of optical phenomena generated in molecule-based magnetic materials, including the recent advances in such areas as high-temperature photomagnetism, optical thermometry utilizing SMMs, optical addressability of molecular qubits, magneto-chiral dichroism, and opto-magneto-electric multifunctionality. These findings are discussed in the context of the types of optical phenomena accessible for various classes of molecule-based magnetic materials.

ExROPPP: Fast, accurate, and spin-pure calculation of the electronically excited states of organic hydrocarbon radicals.

Recent years have seen an explosion of interest in organic radicals due to their promise for highly efficient organic light-emitting diodes and molecular qubits. However, accurately and inexpensively computing their electronic structure has been challenging, especially for excited states, due to the spin-contamination problem. Furthermore, while alternacy or "pseudoparity" rules have guided the interpretation and prediction of the excited states of closed-shell hydrocarbons since the 1950s, similar general rules for hydrocarbon radicals have not to our knowledge been found yet. In this article, we present solutions to both of these challenges. First, we combine the extended configuration interaction singles method with Pariser-Parr-Pople (PPP) theory to obtain a method that we call ExROPPP (Extended Restricted Open-shell PPP) theory. We find that ExROPPP computes spin-pure excited states of hydrocarbon radicals with comparable accuracy to experiment as high-level general multi-configurational quasi-degenerate perturbation theory calculations but at a computational cost that is at least two orders of magnitude lower. We then use ExROPPP to derive widely applicable rules for the spectra of alternant hydrocarbon radicals, which are completely consistent with our computed results. These findings pave the way for highly accurate and efficient computation and prediction of the excited states of organic radicals.

A novel non-adiabatic spin relaxation mechanism in molecular qubits.

The interaction of electronic spin and molecular vibrations mediated by spin-orbit coupling governs spin relaxation in molecular qubits. We derive an extended molecular spin Hamiltonian that includes both adiabatic and non-adiabatic spin-dependent interactions, and we implement the computation of its matrix elements using state-of-the-art density functional theory. The new molecular spin Hamiltonian contains a novel spin-vibrational orbit interaction with a non-adiabatic origin, together with the traditional molecular Zeeman and zero-field splitting interactions with an adiabatic origin. The spin-vibrational orbit interaction represents a non-Abelian Berry curvature on the ground-state electronic manifold and corresponds to an effective magnetic field in the electronic spin dynamics. We further develop a spin relaxation rate model that estimates the spin relaxation time via the two-phonon Raman process. An application of the extended molecular spin Hamiltonian together with the spin relaxation rate model to Cu(II) porphyrin, a prototypical S = 1/2 molecular qubit, demonstrates that the spin relaxation time at elevated temperatures is dominated by the non-adiabatic spin-vibrational orbit interaction. The computed spin relaxation rate and its magnetic field orientation dependence are in excellent agreement with experimental measurements.