The Transformer model, renowned for its powerful attention mechanism, has achieved state-of-the-art performance in various artificial intelligence tasks but faces challenges with quantum data. With a growing focus on leveraging quantum machine learning for quantum data, particularly in quantum chemistry, we propose the Molecular Quantum Transformer (MQT) for modeling interactions in molecular quantum systems. By utilizing quantum circuits to implement the attention mechanism on the molecular configurations, MQT can efficiently calculate ground-state energies for all configurations. Numerical demonstrations show that in calculating ground-state energies for H2, LiH, BeH2, and H4, MQT outperforms the classical Transformer, highlighting the promise of quantum effects in Transformer structures. Furthermore, its pretraining capability on diverse molecular data facilitates the efficient learning of new molecules, extending its applicability to complex molecular systems with minimal additional effort. Our method offers an alternative to existing quantum algorithms for estimating ground-state energies, opening new avenues in quantum chemistry and materials science.
The Transformer model, renowned for its powerful attention mechanism, has achieved state-of-the-art performance in various artificial intelligence tasks but faces challenges with quantum data. With a growing focus on leveraging quantum machine learning for quantum data, particularly in quantum chemistry, we propose the Molecular Quantum Transformer (MQT) for modeling interactions in molecular quantum systems. By utilizing quantum circuits to implement the attention mechanism on the molecular configurations, MQT can efficiently calculate ground-state energies for all configurations. Numerical demonstrations show that in calculating ground-state energies for H2, LiH, BeH2, and H4, MQT outperforms the classical Transformer, highlighting the promise of quantum effects in Transformer structures. Furthermore, its pretraining capability on diverse molecular data facilitates the efficient learning of new molecules, extending its applicability to complex molecular systems with minimal additional effort. Our method offers an alternative to existing quantum algorithms for estimating ground-state energies, opening new avenues in quantum chemistry and materials science.
Accurate and efficient prediction of electronic wavefunctions is central to ab initio molecular dynamics (AIMD) and electronic structure theory. However, conventional ab initio methods require self-consistent optimization of electronic states at every nuclear configuration, leading to prohibitive computational costs, especially for large or strongly correlated systems. Here, we introduce a quantum-centric machine learning (QCML) model-a hybrid quantum-classical framework that integrates parameterized quantum circuits (PQCs) with Transformer-based machine learning to directly predict molecular wavefunctions and quantum observables. By pretraining the Transformer on a diverse dataset of molecules and ansatz types and subsequently fine-tuning it for specific systems, QCML learns transferable mappings between molecular descriptors and PQC parameters, eliminating the need for iterative variational optimization. The pretrained model achieves chemical accuracy in potential energy surfaces, atomic forces, and dipole moments across multiple molecules and ansatzes, and enables efficient AIMD simulations with infrared spectra prediction. This work establishes a scalable and transferable quantum-centric machine learning paradigm, bridging variational quantum algorithms and modern deep learning for next-generation molecular simulation and quantum chemistry applications.
Correct prediction of the molecular ground-state energy is a fundamental problem in quantum chemistry, materials science and drug screening and discovery which directly impacts the understanding of the stability and chemical behavior of molecules. For complex molecular systems, traditional computational techniques like the Hartree-Fock and the Density Functional Theory (DFT) can be very costly. The improvement of molecular energy prediction efficiency and accuracy has recently opened new possibilities thanks to the progress in quantum computation and deep learning. In this paper, a hybrid Quantum Deep Learning Framework for Accurate Molecular Ground-State Energy Prediction in Complex Chemical Systems combining Variational Quantum Algorithms and Deep Neural Network Architectures is proposed. The framework builds molecular Hamiltonians, optimizes the quantum state with the Variational Quantum Eigensolver (VQE), and builds quantum-generated features for deep learning-based energy estimation. Performance measures used for the evaluation of the proposed model are Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Coefficient of Determination (R²). The proposed Quantum Deep Learning Framework has shown Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and R2 values equal to 0.042, 0.031, and 0.989 correspondingly, which proves higher performance from the standpoint of prediction. Prediction precision of the developed approach reaches 98.9% and exceeds that of all other methods known, including VQE, ADAPT-VQE, FermiNet, and Deep Schrödinger. Besides that, the proposed approach showed faster convergence, lower prediction variance, and higher computational efficiency during the molecular energies' prediction process. The results suggest that the proposed hybrid quantum-classical approach is promising and efficient for ground-state energy prediction of molecules, as well as useful in computational chemistry, materials discovery, and molecular design, and is scalable.
Quantum many-body calculations are fundamentally limited by the exponential growth of the configuration space, making accurate treatment of strongly correlated systems computationally prohibitive. Here we present the Generative Transformer Neural Network Selected Configuration Interaction (GTNN-SCI), a Transformer-based machine learning approach that generatively samples important configurations to accelerate many-body quantum chemistry calculations. By leveraging the Transformer architecture’s self-attention mechanism to capture long-range electron correlations, GTNN-SCI achieves up to 10× speedup compared to state-of-the-art neural network methods while maintaining high accuracy. We demonstrate the efficacy of GTNN-SCI by calculating correlation and binding energies for representative molecules including N 2, H 2 O, and C 2 using both Gaussian (cc-pVDZ) and plane-wave basis sets, achieving faster convergence and lower energies than previously reported neural network-based selected CI techniques. Most significantly, our generative approach identifies higher-order excitations missed by conventional coupling schemes, yielding lower variational energies than established methods including heat-bath CI. This capability enables GTNN-SCI to accurately treat the strongly correlated [Fe 2 S 2 (SCH 3 ) 4 ] 2– ([2Fe–2S]) cluster system, achieving ground-state energies within chemical accuracy of DMRG benchmarks, whereas conventional selected CI methods have failed on this system. The GTNN-SCI method thus combines modern deep learning with high-performance electronic structure computation, providing an efficient and precise avenue for solving the electronic Schrödinger equation in challenging molecular systems.
Abstract Understanding the properties of excited states of complex molecules is crucial for many chemical and physical processes. Calculating these properties is often significantly more resource-intensive than calculating their ground state counterparts. We present a quantum machine learning model that predicts excited-state properties from the molecular ground state for different geometric configurations. The model comprises a symmetry-invariant quantum neural network (NN) and a conventional NN and is able to provide accurate predictions with only a few training data points. The proposed procedure is fully NISQ compatible. This is achieved by using a quantum circuit that requires a number of parameters linearly proportional to the number of molecular orbitals, along with a parameterized measurement observable, thereby reducing the number of necessary measurements. We benchmark the algorithm on three different molecules with three different system sizes: H 2 with four orbitals, LiH with five orbitals, and H 4 with six orbitals. For these molecules, we predict the excited state transition energies and transition dipole moments. We show that, in many cases, the procedure is able to outperform various classical models (support vector machines, Gaussian processes, and NNs) that rely solely on classical features, by up to two orders of magnitude in the test mean squared error.
This research explores the integration of quantum mechanics, machine learning, and quantum computing to advance predictive modeling of nuclear magnetic resonance (NMR) parameters. The aim is to develop a hybrid quantum-enhanced machine learning model that combines the accuracy of quantum calculations with the efficiency of machine learning techniques for predicting NMR chemical shifts. The conceptual framework involves quantum mechanical calculations for accurate reference NMR parameters, supervised machine learning models trained on diverse molecular datasets, and hybrid quantum-classical algorithms to leverage quantum computing resources. A simplified numerical example demonstrates the potential of the proposed model for predicting NMR chemical shifts for small molecular systems. The results showcase the model's ability to capture underlying relationships between molecular features and NMR observables, indicating promise for larger and more complex systems. This interdisciplinary approach opens new avenues for advancing NMR spectroscopy and understanding molecular structures, dynamics, and interactions in various scientific domains. The research also discusses challenges and opportunities in integrating quantum mechanics, machine learning, and quantum computing, emphasizing the importance of diverse datasets and quantum algorithm selection. The proposed model holds significant implications for transforming NMR parameter predictions and contributing to chemistry, biochemistry, and materials science research
Abstract This paper addresses the challenge of accurately predicting the ground-state energy of the hydrogen molecule (H2), a fundamental problem in quantum chemistry that demands high precision and efficient computation. Traditional classical methods, such as Full Configuration Interaction (FCI), provide accurate results but are computationally expensive and scale poorly with system size. To overcome these limitations, we propose a hybrid quantum-classical approach based on Quantum Neural Networks (QNNs) trained on high-precision FCI data. Our method encodes interatomic distances into parameterized quantum circuits and employs classical optimization to learn the complex energy landscape of H2 across a wide range of molecular geometries. The QNN model achieves energy predictions that closely match reference FCI values with minimal deviation, while significantly reducing quantum resource requirements compared to conventional quantum algorithms. This work demonstrates the potential of QNNs as scalable and efficient tools for quantum chemistry, laying the groundwork for future applications to larger and more complex molecular systems.