An equivariant generative framework for molecular graph-structure Co-design.

Designing molecules with desirable physiochemical properties and functionalities is a long-standing challenge in chemistry, material science, and drug discovery. Recently, machine learning-based generative models have emerged as promising approaches for de novo molecule design. However, further refinement of methodology is highly desired as most existing methods lack unified modeling of 2D topology and 3D geometry information and fail to effectively learn the structure-property relationship for molecule design. Here we present MolCode, a roto-translation equivariant generative framework for molecular graph-structure Co-design. In MolCode, 3D geometric information empowers the molecular 2D graph generation, which in turn helps guide the prediction of molecular 3D structure. Extensive experimental results show that MolCode outperforms previous methods on a series of challenging tasks including de novo molecule design, targeted molecule discovery, and structure-based drug design. Particularly, MolCode not only consistently generates valid (99.95% validity) and diverse (98.75% uniqueness) molecular graphs/structures with desirable properties, but also generates drug-like molecules with high affinity to target proteins (61.8% high affinity ratio), which demonstrates MolCode's potential applications in material design and drug discovery. Our extensive investigation reveals that the 2D topology and 3D geometry contain intrinsically complementary information in molecule design, and provide new insights into machine learning-based molecule representation and generation.

Variational Quantum-Neural Hybrid Eigensolver.

The variational quantum eigensolver (VQE) is one of the most representative quantum algorithms in the noisy intermediate-scale quantum (NISQ) era, and is generally speculated to deliver one of the first quantum advantages for the ground-state simulations of some nontrivial Hamiltonians. However, short quantum coherence time and limited availability of quantum hardware resources in the NISQ hardware strongly restrain the capacity and expressiveness of VQEs. In this Letter, we introduce the variational quantum-neural hybrid eigensolver (VQNHE) in which the shallow-circuit quantum Ansatz can be further enhanced by classical post-processing with neural networks. We show that the VQNHE consistently and significantly outperforms the VQE in simulating ground-state energies of quantum spins and molecules given the same amount of quantum resources. More importantly, we demonstrate that, for arbitrary postprocessing neural functions, the VQNHE only incurs a polynomial overhead of processing time and represents the first scalable method to exponentially accelerate the VQE with nonunitary postprocessing that can be efficiently implemented in the NISQ era.

Variational Quantum Simulation of Chemical Dynamics with Quantum Computers.

Classical simulations of real-space quantum dynamics are challenging due to the exponential scaling of computational cost with system dimensions. Quantum computers offer the potential to simulate quantum dynamics with polynomial complexity; however, existing quantum algorithms based on the split-operator techniques require large-scale fault-tolerant quantum computers that remain elusive in the near future. Here, we present variational simulations of real-space quantum dynamics suitable for implementation in noisy intermediate-scale quantum (NISQ) devices. The Hamiltonian is first encoded onto qubits using a discrete variable representation and binary encoding scheme. We show that direct application of a real-time variational quantum algorithm based on the McLachlan's principle is inefficient as the measurement cost grows exponentially with the qubit number for general potential energy, and an extremely small time-step size is required to achieve accurate results. Motivated by the insights that many chemical dynamics occur in the low-energy subspace, we propose a subspace expansion method by projecting the total Hamiltonian, including the time-dependent driving field, onto the system low-energy eigenstate subspace using quantum computers, and the exact quantum dynamics within the subspace can then be solved classically. We show that the measurement cost of the subspace approach grows polynomially with dimensionality for general potential energy. Our numerical examples demonstrate the capability of our approach, even under intense laser fields. Our work opens the possibility of simulating chemical dynamics with NISQ hardware.

Simulating Energy Transfer in Molecular Systems with Digital Quantum Computers.

Quantum computers have the potential to simulate chemical systems beyond the capability of classical computers. Recent developments in hybrid quantum-classical approaches enable the determinations of the ground or low energy states of molecular systems. Here, we extend near-term quantum simulations of chemistry to time-dependent processes by simulating energy transfer in organic semiconducting molecules. We developed a multiscale modeling workflow that combines conventional molecular dynamics and quantum chemistry simulations with hybrid variational quantum algorithm to compute the exciton dynamics in both the single excitation subspace (i.e., Frenkel Hamiltonian) and the full-Hilbert space (i.e., multiexciton) regimes. Our numerical examples demonstrate the feasibility of our approach, and simulations on IBM Q devices capture the qualitative behaviors of exciton dynamics, but with considerable errors. We present an error mitigation technique that combines experimental results from the variational and Trotter algorithms, and obtain significantly improved quantum dynamics. Our approach opens up new opportunities for modeling quantum dynamics in chemical, biological, and material systems with quantum computers.

Simulation of Condensed-Phase Spectroscopy with Near-Term Digital Quantum Computers.

Spectroscopy is an indispensable tool for understanding the structures and dynamics of molecular systems. However, computational modeling of spectroscopy is challenging due to the exponential scaling of computational complexity with system sizes unless drastic approximations are made. Quantum computers could potentially overcome these classically intractable computational tasks, but the existing approaches using quantum computers to simulate spectroscopy can only handle isolated and static molecules. In this work, we develop a workflow that combines multi-scale modeling and a time-dependent variational quantum algorithm to compute the linear spectroscopy of systems interacting with their condensed-phase environment via the relevant time correlation function. We demonstrate the feasibility of our approach by numerically simulating the UV-vis absorption spectra of organic semiconductors. We show that our dynamical approach captures several spectral features that are otherwise overlooked by static methods. Our method can be directly used for other linear condensed-phase spectroscopy and could potentially be extended to nonlinear multi-dimensional spectroscopy.

Transfer learning with graph neural networks for optoelectronic properties of conjugated oligomers.

Despite the remarkable progress of machine learning (ML) techniques in chemistry, modeling the optoelectronic properties of long conjugated oligomers and polymers with ML remains challenging due to the difficulty in obtaining sufficient training data. Here, we use transfer learning to address the data scarcity issue by pre-training graph neural networks using data from short oligomers. With only a few hundred training data, we are able to achieve an average error of about 0.1 eV for the excited-state energy of oligothiophenes against time-dependent density functional theory (TDDFT) calculations. We show that the success of our transfer learning approach relies on the relative locality of low-lying electronic excitations in long conjugated oligomers. Finally, we demonstrate the transferability of our approach by modeling the lowest-lying excited-state energies of poly(3-hexylthiophene) in its single-crystal and solution phases using the transfer learning models trained with the data of gas-phase oligothiophenes. The transfer learning predicted excited-state energy distributions agree quantitatively with TDDFT calculations and capture some important qualitative features observed in experimental absorption spectra.

Machine learning Frenkel Hamiltonian parameters to accelerate simulations of exciton dynamics.

In this manuscript, we develop multiple machine learning (ML) models to accelerate a scheme for parameterizing site-based models of exciton dynamics from all-atom configurations of condensed phase sexithiophene systems. This scheme encodes the details of a system's specific molecular morphology in the correlated distributions of model parameters through the analysis of many single-molecule excited-state electronic-structure calculations. These calculations yield excitation energies for each molecule in the system and the network of pair-wise intermolecular electronic couplings. Here, we demonstrate that the excitation energies can be accurately predicted using a kernel ridge regression (KRR) model with Coulomb matrix featurization. We present two ML models for predicting intermolecular couplings. The first one utilizes a deep neural network and bi-molecular featurization to predict the coupling directly, which we find to perform poorly. The second one utilizes a KRR model to predict unimolecular transition densities, which can subsequently be analyzed to compute the coupling. We find that the latter approach performs excellently, indicating that an effective, generalizable strategy for predicting simple bimolecular properties is through the indirect application of ML to predict higher-order unimolecular properties. Such an approach necessitates a much smaller feature space and can incorporate the insight of well-established molecular physics.

Representing the Molecular Signatures of Disordered Molecular Semiconductors in Size-Extendable Models of Exciton Dynamics.

This manuscript presents an approach to developing size-extendable phenomenological site-based models for simulating exciton dynamics in disordered organic molecular semiconducting materials. This approach extends an existing methodology that assigns the parameters of the time-dependent Frenkel exciton model by applying fragmentation-based electronic structure calculations to the output of classical molecular dynamics simulations. This methodology is inherently limited by the system size of the all-atom simulation, which is well below the performance capability of site-based models. Here, we demonstrate that this system size limitation can be effectively overcome by defining a size-extendable surrogate model based on the correlated parameter statistics derived from existing fragmentation-based methods. We demonstrate our approach on a monolayer film of sexithiophene molecules, first validating the accuracy of the surrogate system in reproducing exciton dynamical properties of a 150 molecule system, then extending it to systems of 2500 molecules. With this extended system, we explore the sensitivity of exciton dynamics to variations in the temperature as well as the amplitude and spatial correlations of energetic disorder. We conclude that exciton dynamics can be significantly enhanced in morphologies with spatially correlated molecular configurations but only if the overall distribution of site energies is sufficiently broad.

Terahertz-Driven Stark Spectroscopy of CdSe and CdSe-CdS Core-Shell Quantum Dots.

The effects of large external fields on semiconductor nanostructures could reveal much about field-induced shifting of electronic states and their dynamical responses and could enable electro-optic device applications that require large and rapid changes in optical properties. Studies of quasi-dc electric field modulation of quantum dot (QD) properties have been limited by electrostatic breakdown processes observed under high externally applied field levels. To circumvent this, here we apply ultrafast terahertz (THz) electric fields with switching times on the order of 1 ps. We show that a pulsed THz electric field, enhanced by a microslit field enhancement structure (FES), can strongly manipulate the optical absorption properties of a thin film of CdSe and CdSe-CdS core-shell QDs on the subpicosecond time scale with spectral shifts that span the visible to near-IR range. Numerical simulations using a semiempirical tight binding model show that the band gap of the QD film can be shifted by as much a 79 meV during these time scales. The results allow a basic understanding of the field-induced shifting of electronic levels and suggest electro-optic device applications.

Environment mediated multipartite and multidimensional entanglement.

Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling strengths multipartite entanglement may form between qubits and between higher spins, i.e., qudits. We characterise the multipartite entanglement using an entanglement witness based upon the structure factor and demonstrate its validity versus the directly calculated entanglement of formation, suggesting possible experiments for its measure.

The Enhancement of Interfacial Exciton Dissociation by Energetic Disorder Is a Nonequilibrium Effect.

The dissociation of excited electron-hole pairs is a microscopic process that is fundamental to the performance of photovoltaic systems. For this process to be successful, the oppositely charged electron and hole must overcome an electrostatic binding energy before they undergo ground state recombination. It has been observed previously that the presence of energetic disorder can lead to a reduction in recombination losses. Here we investigate this effect using a simple model of charge dynamics at a donor-acceptor interface. We consider the effect of spatial variations in electronic energy levels, such as those that arise in disordered molecular systems, on dissociation yield and demonstrate that it is maximized with a finite amount of disorder. We demonstrate that this is a nonequilibrium effect that is mediated by the dissipation driven formation of partially dissociated intermediate states that are long-lived because they cannot easily recombine. We present a kinetic model that incorporates these states and show that it is capable of reproducing similar behavior when it is parametrized with nonequilibrium rates.

Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition.

The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D limits. It is found that the scaling relation is universal and independent of the temperature, disorder, and noise parameters, and the essential order parameter is the ratio between the localization length in 2D and the circumference of the tube. Phenomenological and quantitative expressions for transport properties as functions of disorder and noise are obtained and applied to real systems: In the natural chlorosomes found in light-harvesting bacteria the exciton transfer dynamics is predicted to be in the 2D limit, whereas a family of synthetic molecular aggregates is found to be in the homogeneous limit and is independent of dimensionality.

A Model of Charge-Transfer Excitons: Diffusion, Spin Dynamics, and Magnetic Field Effects.

In this Letter, we explore how the microscopic dynamics of charge-transfer (CT) excitons are influenced by the presence of an external magnetic field in disordered molecular semiconductors. This influence is driven by the dynamic interplay between the spin and spatial degrees of freedom of the electron-hole pair. To account for this interplay, we have developed a numerical framework that combines a traditional model of quantum spin dynamics with a stochastic coarse-grained model of charge transport. This combination provides a general and efficient methodology for simulating the effects of magnetic field on CT state dynamics, therefore providing a basis for revealing the microscopic origin of experimentally observed magnetic field effects. We demonstrate that simulations carried out on our model are capable of reproducing experimental results as well as generating theoretical predictions related to the efficiency of organic electronic materials.

Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport.

Quantum transport in disordered systems is studied using a polaron-based master equation. The polaron approach is capable of bridging the results from the coherent band-like transport regime governed by the Redfield equation to incoherent hopping transport in the classical regime. A non-monotonic dependence of the diffusion coefficient is observed both as a function of temperature and system-phonon coupling strength. In the band-like transport regime, the diffusion coefficient is shown to be linearly proportional to the system-phonon coupling strength and vanishes at zero coupling due to Anderson localization. In the opposite classical hopping regime, we correctly recover the dynamics described by the Fermi's Golden Rule and establish that the scaling of the diffusion coefficient depends on the phonon bath relaxation time. In both the hopping and band-like transport regimes, it is demonstrated that at low temperature, the zero-point fluctuations of the bath lead to non-zero transport rates and hence a finite diffusion constant. Application to rubrene and other organic semiconductor materials shows a good agreement with experimental mobility data.

Noncanonical statistics of a spin-boson model: theory and exact Monte Carlo simulations.

Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid, and equilibrium quantum statistics of the system may be noncanonical. By exploiting both polaron transformation and perturbation theory in a spin-boson model, an analytical treatment is advocated to study noncanonical statistics of a two-level system at arbitrary temperature and for arbitrary SBC strength, yielding theoretical results in agreement with exact Monte Carlo simulations. In particular, the eigen-representation of system's reduced density matrix is used to quantify noncanonical statistics as well as the quantumness of the open system. For example, it is found that irrespective of SBC strength, noncanonical statistics enhances as temperature decreases but vanishes at high temperature.

Excitonic energy transfer in light-harvesting complexes in purple bacteria.

Two distinct approaches, the Frenkel-Dirac time-dependent variation and the Haken-Strobl model, are adopted to study energy transfer dynamics in single-ring and double-ring light-harvesting (LH) systems in purple bacteria. It is found that the inclusion of long-range dipolar interactions in the two methods results in significant increase in intra- or inter-ring exciton transfer efficiency. The dependence of exciton transfer efficiency on trapping positions on single rings of LH2 (B850) and LH1 is similar to that in toy models with nearest-neighbor coupling only. However, owing to the symmetry breaking caused by the dimerization of BChls and dipolar couplings, such dependence has been largely suppressed. In the studies of coupled-ring systems, both methods reveal an interesting role of dipolar interactions in increasing energy transfer efficiency by introducing multiple intra/inter-ring transfer paths. Importantly, the time scale (4 ps) of inter-ring exciton transfer obtained from polaron dynamics is in good agreement with previous studies. In a double-ring LH2 system, non-nearest neighbor interactions can induce symmetry breaking, which leads to global and local minima of the average trapping time in the presence of a non-zero dephasing rate, suggesting that environment dephasing helps preserve quantum coherent energy transfer when the perfect circular symmetry in the hypothetic system is broken. This study reveals that dipolar coupling between chromophores may play an important role in the high energy transfer efficiency in the LH systems of purple bacteria and many other natural photosynthetic systems.

Accuracy of second order perturbation theory in the polaron and variational polaron frames.

In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters.

Fokker-Planck equation with arbitrary dc and ac fields: continued fraction method.

The continued fraction method (CFM) is used to solve the Fokker-Planck equation with arbitrary dc and ac fields. With an appropriate choice of basis functions, the Fokker-Planck equation is converted into a set of linear algebraic equations with short-ranged coupling and then CFM is implemented to obtain numerical solutions with high efficiency. Both a proposed perturbative CFM and the numerically exact matrix CFM are used to study the nonlinear response of driven systems, with their results compared to assess the validity regime of the perturbative approach. The proposed perturbative CFM approach needs scalar quantities only and hence is more efficient within its validity regime. Two nonlinear systems of different nature are used as examples: molecular dipole (rotational Brownian motion) and particle in a periodic potential (translational Brownian motion). The associated full dynamics is presented in the compact form of hysteresis loops. It is observed that as the strength of an AC driving field increases, pronounced nonlinear effects are manifested in the deformation of the hysteresis loops.