Practical application of quantum neural network to materials informatics.

Quantum neural network (QNN) models have received increasing attention owing to their strong expressibility and resistance to overfitting. It is particularly useful when the size of the training data is small, making it a good fit for materials informatics (MI) problems. However, there are only a few examples of the application of QNN to multivariate regression models, and little is known about how these models are constructed. This study aims to construct a QNN model to predict the melting points of metal oxides as an example of a multivariate regression task for the MI problem. Different architectures (encoding methods and entangler arrangements) are explored to create an effective QNN model. Shallow-depth ansatzs could achieve sufficient expressibility using sufficiently entangled circuits. The "linear" entangler was adequate for providing the necessary entanglement. The expressibility of the QNN model could be further improved by increasing the circuit width. The generalization performance could also be improved, outperforming the classical NN model. No overfitting was observed in the QNN models with a well-designed encoder. These findings suggest that QNN can be a useful tool for MI.

Computational Analysis of Chemical Reactions Using a Variational Quantum Eigensolver Algorithm without Specifying Spin Multiplicity.

The analysis of a chemical reaction along the ground-state potential energy surface in conjunction with an unknown spin state is challenging because electronic states must be separately computed several times using different spin multiplicities to find the lowest energy state. However, in principle, the ground state could be obtained with just a single calculation using a quantum computer without specifying the spin multiplicity in advance. In the present work, ground-state potential energy curves for PtCO were calculated as a proof-of-concept using a variational quantum eigensolver (VQE) algorithm. This system exhibits a singlet-triplet crossover as a consequence of the interaction between Pt and CO. VQE calculations using a statevector simulator were found to converge to a singlet state in the bonding region, while a triplet state was obtained at the dissociation limit. Calculations performed using an actual quantum device provided potential energies within ±2 kcal/mol of the simulated energies after error mitigation techniques were adopted. The spin multiplicities in the bonding and dissociation regions could be clearly distinguished even in the case of a small number of shots. The results of this study suggest that quantum computing can be a powerful tool for the analysis of the chemical reactions of systems for which the spin multiplicity of the ground state and variations in this parameter are not known in advance.

Discovering surface reaction pathways using accelerated molecular dynamics and network analysis tools.

We present an automated method that maps surface reaction pathways with no experimental data and with minimal human interventions. In this method, bias potentials promoting surface reactions are applied to enable statistical samplings of the surface reaction within the timescale of ab initio molecular dynamics (MD) simulations, and elementary reactions are extracted automatically using an extension of the method constructed for gas- or liquid-phase reactions. By converting the extracted elementary reaction data to directed graph data, MD trajectories can be efficiently mapped onto reaction pathways using a network analysis tool. To demonstrate the power of the method, it was applied to the steam reforming of methane on the Rh(111) surface and to propane reforming on the Pt(111) and Pt3Sn(111) surfaces. We discover new energetically favorable pathways for both reactions and reproduce the experimentally-observed materials-dependence of the surface reaction activity and the selectivity for the propane reforming reactions.

Mechanisms of temperature-dependent oxygen absorption/release and appearance of intermediate phase in κ-Ce2Zr2O8: study based on oxygen vacancy formation energy computations.

This study clarified the mechanisms of the temperature-dependent oxygen absorption/release properties and appearance of the intermediate phase for κ-Ce2Zr2O8, which is known to have a high oxygen storage/release capacity (OSC). First-principle computations revealed that the vacancy formation energies depend on the number of vacancies and can be categorized into two groups: low-energy and high-energy. The intermediate phase observed experimentally was assigned to the state after all the oxygen vacancies in the low-energy group were formed. We also found that the mechanism of the improved OSC performance by Ti substitution could be explained in terms of the vacancy formation energies.

Molecular Structure Optimization Based on Electrons-Nuclei Quantum Dynamics Computation.

A new concept of the molecular structure optimization method based on quantum dynamics computations is presented. Nuclei are treated as quantum mechanical particles, as are electrons, and the many-body wave function of the system is optimized by the imaginary time evolution method. The numerical demonstrations with a two-dimensional H2 + system and a H-C-N system exemplify two possible advantages of our proposed method: (1) the optimized nuclear positions can be specified with a small number of observations (quantum measurements) and (2) the global minimum structure of nuclei can be obtained without starting from any sophisticated initial structure and getting stuck in the local minima. This method is considered to be suitable for quantum computers, the development of which will realize its application as a powerful method.

Calculation of Core-Excited and Core-Ionized States Using Variational Quantum Deflation Method and Applications to Photocatalyst Modeling.

The possibility of performing quantum-chemical calculations using quantum computers has attracted much interest. Variational quantum deflation (VQD) is a quantum-classical hybrid algorithm for the calculation of excited states with noisy intermediate-scale quantum devices. Although the validity of this method has been demonstrated, there have been few practical applications, primarily because of the uncertain effect of calculation conditions on the results. In the present study, calculations of the core-excited and core-ionized states for common molecules based on the VQD method were examined using a classical computer, focusing on the effects of the weighting coefficients applied in the penalty terms of the cost function. Adopting a simplified procedure for estimating the weighting coefficients based on molecular orbital levels allowed these core-level states to be successfully calculated. The O 1s core-ionized state for a water molecule was calculated with various weighting coefficients, and the resulting ansatz states were systematically examined. The application of this technique to functional materials was demonstrated by calculating the core-level states for titanium dioxide (TiO2) and nitrogen-doped TiO2 models. The results demonstrate that VQD calculations employing an appropriate cost function can be applied to the analysis of functional materials in conjunction with an experimental approach.

Practical hyperdynamics method for systems with large changes in potential energy.

A practical hyperdynamics method is proposed to accelerate systems with highly endothermic and exothermic reactions such as hydrocarbon pyrolysis and oxidation reactions. In this method, referred to as the "adaptive hyperdynamics (AHD) method," the bias potential parameters are adaptively updated according to the change in potential energy. The approach is intensively examined for JP-10 (exo-tetrahydrodicyclopentadiene) pyrolysis simulations using the ReaxFF reactive force field. Valid boost parameter ranges are clarified as a result. It is shown that AHD can be used to model pyrolysis at temperatures as low as 1000 K while achieving a boost factor of around 10(5).

A time-dependent density-functional approach to nonadiabatic electron-nucleus dynamics: formulation and photochemical application.

To study nonadiabatic dynamics of the electrons and nuclei, the quantum chemical wavefunction methods have often been invoked to compute the nonadiabatic couplings (NACs), but time-dependent density functional theory (TD-DFT) can provide a formally exact alternative approach when the ground and one excited electronic states are concerned. Based on the density response scheme to compute the NAC vectors [J. Chem. Phys., 2007, 127, 064103], herein presented are a full quantum wave packet and a semi-classical surface hopping approach to the nonadiabatic chemical reactions for the electronically ground and excited states. The adiabatic local density approximation (ALDA) was used here but, contrary to previous simulations based on DFT or TD-DFT, no further approximations were made for the electrons. With those approaches we could successfully describe the photochemical syn-anti isomerization dynamics of a formaldimine molecule (CH2=NH) and investigate the dissipation effects with use of a Langevin dynamics scheme. These simulations demonstrated an important role played by the dissipation and suggested that accurately modeling the dissipation is the next step towards a truly ab initio prediction.

Nonadiabatic couplings from time-dependent density functional theory. II. Successes and challenges of the pseudopotential approximation.

We present extensive calculations of nonadiabatic couplings (NACs) between the electronically ground and excited states of molecules, using time-dependent density functional theory (TDDFT) within (modified) linear response [C. Hu et al. J. Chem. Phys. 127, 064103 (2007)]. Our approach is implemented in the pseudopotential framework, with the consideration of nonlinear core corrections. The features of either the ordinary Jahn-Teller conical intersections in X(3) (X=Li, Na, K, Cu, Ag, Au) trimers, or the elliptic Jahn-Teller conical intersections in NaH(2), have been well reproduced. In particular, anticipated results for the H-H(2) collision near the avoided crossing are obtained, showing appealing improvement over the first, real-time, TDDFT calculation. The other important type of intersections, Renner-Teller glancing intersection, has also been studied for several typical molecular systems (BH(2), AlH(2), CH(2)(+), SiH(2)(+)), giving results in reasonable agreement with the theoretical model. Despite these successes, it is found that for some systems, including both Jahn-Teller and Renner-Teller systems, the pseudopotential scheme might give inaccurate results for some NAC components on nonhydrogen atoms. By trying different construction schemes of pseudopotentials, e.g., using local pseudopotentials, the results of NACs are found scheme-dependent and show improvement for some cases. Since there is much freedom in constructing ab initio nonlocal pseudopotentials, our findings on TDDFT calculation of NACs in the pseudopotential scheme might be helpful to give clues for constructing more "realistic" pseudopotentials.

Nonadiabatic couplings from time-dependent density functional theory: formulation in the Casida formalism and practical scheme within modified linear response.

We present an efficient method to compute nonadiabatic couplings (NACs) between the electronically ground and excited states of molecules, within the framework of time-dependent density functional theory (TDDFT) in frequency domain. Based on the comparison of dynamic polarizability formulated both in the many-body wave function form and the Casida formalism, a rigorous expression is established for NACs, which is similar to the calculation of oscillator strength in the Casida formalism. The adiabatic local density approximation (ALDA) gives results in reasonable accuracy as long as the conical intersection (ci) is not approached too closely, while its performance quickly degrades near the ci point. This behavior is consistent with the real-time TDDFT calculation. Through the use of modified linear response theory together with the ground-state-component separation scheme, the performance of ALDA can be greatly improved, not only in the vicinity of ci but also for Rydberg transitions and charge-transfer excitations. Several calculation examples, including the quantization of NACs from the Jahn-Teller effect in the H3 system, have been given to show that TDDFT can efficiently give NACs with an accuracy comparable to that of wave-function-based methods.