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.
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 Computing (QC) offers outstanding potential for molecular characterization and drug discovery, particularly in solving complex properties like the Ground State Energy (GSE) of biomolecules. However, QC faces challenges due to computational noise, scalability, and system complexity. This work presents a hybrid framework combining Machine Learning (ML) techniques with quantum algorithms−Variational Quantum Eigensolver (VQE), Hartree-Fock (HF), and Quantum Phase Estimation (QPE)−to improve GSE predictions for large molecules. Three datasets (chemical descriptors, Coulomb matrices, and a hybrid combination) were prepared using molecular features from PubChem. These datasets trained XGBoost (XGB), Random Forest (RF), and LightGBM (LGBM) models. XGB achieved the lowest Relative Error (RE) of 4.41±11.18% on chemical descriptors, outperforming RF (5.56±11.66%) and LGBM (5.32±12.87%). HF delivered exceptional precision for small molecules (0.44±0.66%RE), while a near-linear correlation between GSE and molecular electron count provided predictive shortcuts. This study demonstrates that integrating QC and ML enhances scalability for molecular energy predictions and lays the foundation for scaling QC molecular simulations to larger systems.
Hybrid artificial intelligence–quantum (AI–Q) models arise at the intersection of two rapidly advancing computational paradigms, promising unprecedented capabilities for real-time molecular structure prediction. In classical computational chemistry, the accurate determination of ground-state energies and optimized geometries relies on ab initio methods such as density functional theory (DFT) and coupled-cluster approaches, which, while highly precise, exhibit steep polynomial or exponential scaling with system size. Conversely, deep neural networks (DNNs) have demonstrated remarkable success in learning potential energy surfaces (PES) from large datasets, achieving rapid inference but sometimes lacking the ultimate chemical accuracy required for predictive applications in drug discovery or materials design. On the other hand, variational quantum eigensolvers (VQEs) leverage the intrinsic parallelism of quantum hardware to approximate electronic structure problems, yet they remain constrained by qubit coherence times, gate fidelities, and circuit depth limitations inherent to noisy intermediate-scale quantum (NISQ) devices.
Accurate prediction of molecular structures and properties is vital for chemistry; materials science, and drug discovery, yet classical electronic-structure methods often fail for strongly correlated systems, large basis sets, and complex potential-energy landscapes. Quantum technology encompassing quantum computing, quantum machine learning, and hybrid quantum classical strategies offers a fundamentally new paradigm by encoding many-electron wave functions directly on qubits and exploiting superposition and entanglement to explore exponentially large Hilbert spaces. This review synthesizes recent algorithmic and hardware advances relevant to molecular modelling, including the Variational Quantum Eigensolver (VQE), Quantum Phase Estimation (QPE), quantum unitary coupled-cluster (q-UCC) families, equation-of-motion and subspace methods for excited states, tensor-network hybrids, and quantum kernel and variational QML approaches. We examine noise-aware hybrid workflows, error-mitigation techniques, symmetry-preserving ansätze, and operator-factorization methods that reduce measurement and gate overhead. Representative applications are discussed: ground- and excited-state energy prediction, potential-energy surface mapping, geometry and transition-state optimization, spectroscopic property estimation (IR, UV–Vis, NMR, EPR), and reaction-dynamics scenarios where non-adiabatic effects and conical intersections dominate. Resource estimates and scaling analyses clarify current NISQ limitations qubit counts, circuit depth, shot complexity and delineate the roadmap to fault-tolerant QPE for chemical accuracy. We compare quantum approaches with classical baselines (DFT, CCSD (T), multireference methods), identifying domains where quantum methods already show promise (strong correlation, multi-reference dissociation, spin-state ordering) and where classical methods remain competitive. Finally, we highlight near-term industrial opportunities in drug design, catalysis, CO2 capture, and energy materials, and outline critical research directions: algorithmic reductions in measurement/precision cost, hardware improvements in fidelity and connectivity, scalable ansatz design, and integrated software stacks for reproducible hybrid simulations. Together, these developments indicate that while practical, large-scale quantum advantage for general chemistry remains future work, quantum technologies are rapidly maturing into powerful tools for targeted molecular problems that are intractable with existing classical techniques.
Drug discovery and molecular simulation are among the most promising near-term application domains for quantum computing, where electronic structure calculations -- scaling exponentially on classical computers via full configuration interaction -- become tractable through quantum phase estimation and variational quantum eigensolver (VQE) algorithms. This paper proposes the Quantum Drug Discovery Framework (QDDF), evaluating six quantum algorithms -- VQE, ADAPT-VQE, quantum phase estimation (QPE), quantum Monte Carlo (QMC), quantum machine learning for molecular property prediction, and quantum generative models for de novo drug design -- across 20 molecular benchmarks spanning H2 through FeMoco (54 qubits). Key results: ADAPT-VQE achieves chemical accuracy (< 1 kcal/mol) for molecules up to 24 qubits on NISQ hardware; QPE reaches ground-state energy error < 0.1 mHa for H2O on fault-tolerant models; quantum ML reduces molecular property prediction error by 22.4% versus classical graph neural networks. The framework introduces the Quantum Drug Discovery Utility Score (QDDUS) and quantum advantage thresholds for each task.
Classical machine learning models and quantum kernel methods often struggle to capture quantum-coherent molecular features under the constraints of noisy intermediate-scale quantum (NISQ) hardware, limiting both predictive accuracy and scalability. This paper introduces the Molecular Quantum Particle Algorithm (MQPA), a hybrid quantum–classical framework designed to achieve chemically accurate property prediction by integrating handcrafted molecular descriptors with parameterized quantum circuits. Molecular inputs, expressed as SMILES strings, are processed via RDKit and encoded through angle-based quantum gates with entangling layers in Qiskit [1]. Quantum parameters are optimized using simultaneous perturbation stochastic approximation (SPSA) [2], while classical regression layers leverage Adam [3] with Low-Rank Adaptation (LoRA) fine-tuning [4]. Across 38 systematically varied subsets of the QM9 benchmark [5,6], MQPA achieves a mean absolute error (MAE) of 0.03 kcal/mol, outperforming both deep learning and quantum kernel baselines by 41% and surpassing the chemical accuracy threshold of 0.1 kcal/mol [7–9]. Extensive cross-platform benchmarking—including IBM Quantum, Qiskit Aer, and NVIDIA H100 clusters—demonstrates strong reproducibility, with inter-backend MAE variance below 3%. Positioned as a scalable and hardware-aware solution, MQPA offers practical advantages for quantum-enhanced molecular property prediction across applications in quantum chemistry, drug discovery, materials design, and environmental modeling.
The potential energy surface (PES) is crucial for interpreting a variety of chemical reaction processes. However, predicting accurate PESs with high-level electronic structure methods is a challenging task due to the high computational cost. As an appealing application of quantum computing, we show in this work that variational quantum algorithms can be integrated with machine learning (ML) techniques as a promising scheme for exploring accurate PESs. Different from using a ML model to represent the potential energy, we encode the molecular geometry information into a deep neural network (DNN) to represent parameters of the variational quantum eigensolver (VQE), leaving the PES to the wave function ansatz. Once the DNN model is trained, the variational optimization procedure that hinders the application of the VQE to complex systems is avoided, and thus the evaluation of PESs is significantly accelerated. Numerical results demonstrate that a simple DNN model is able to reproduce accurate PESs for small molecules.