Prediction of the Ground State Energy of the Hydrogen Molecule using Quantum Neural Networks

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.