Hybrid Quantum-classical Strategies for Hydrogen Variational Quantum Eigensolver Optimization

This research focuses on enhancing the optimization process of the classical ground state energy for hydrogen molecules, which is known to be -1.1373 Ha. Various well-known optimization algorithms such as Gradient Descent Optimizer, Adagrad Optimizer, Adam Optimizer, RMSProp Optimizer, and Momentum Optimizer are employed to explore their convergence behavior and their proximity to the precise ground state energy. The analysis extends to examining potential energy curves to gain insights into the stability and reactivity of hydrogen molecules. A notable discovery is the outstanding performance of the Momentum Optimizer, which outperforms other algorithms by achieving a ground state energy of -1.13724 Ha after 40 steps. This consistent and exceptional performance establishes the Momentum Optimizer as the preferred choice. Additionally, a sensitivity analysis of parameters highlights the Momentum Optimizer's unique capability to avoid local minima, reinforcing its importance in optimizing quantum chemistry problems. Importantly, our sensitivity analysis consistently demonstrates the Momentum Optimizer's remarkable and reliable convergence to the exact ground state, irrespective of initial parameter settings. In summary, the study underscores the critical role of the Momentum Optimizer in navigating the complex energy landscapes specific to hydrogen molecules in quantum chemistry simulations.