Estimation of Ground State Energy of Small Molecules and Energy Profile of CO₂ interaction with NH₃ using the Variational Quantum Eigensolver

We benchmark the Variational Quantum Eigensolver (VQE) for computing the ground state energy of small molecules and the reaction profile of CO₂ interaction with NH₃. The Phyton-based Qiskit software package was implemented on the National Energy Technology Laboratory (NETL) Joule 2 supercomputer for the energetic calculations. With the minimal STO-3G basis set, we were able to push our hardware to use to up to 16 qubits on a quantum simulator. While it is possible to simulate H₂, LiH, BeH₂, H₂O and NH₃ with the all-electron approach, the frozen-core approximation has to be used for the bigger CO, CH₄, F₂ and HCl molecules in order to stay in the limit of 16 qubits. All the VQE predicted ground state energies compare well with the full-configuration interaction (FCI) reference values though generally not close to chemical accuracy. We benchmark the VQE-based Hartree Fock-Embedding algorithm to quantify the energy profile of CO₂ + NH₃ = NH₂COOH conversion, a simple CO₂ capture reaction system. The embedding technique allows substantial reduction of classical resources, allowing this more challenging case to be done on classical quantum simulator. The generated reaction profile is found to be in good agreement with the classical high-level CCSD results. We also calculate the vibrational ground state energies of reactants and products along the CO₂ capture reaction pathway using VQE-based technique. The quantum computing algorithm helps enhance the calculation of vibrational ground state energy by considering the many-body vibrational coupling or anharmonicity effect. We describe the many-body potential energy with the expansion to the fourth order using Vibrational Self-Consistent Field method. We demonstrate that the quantum computed ground state energies have similar accuracy for CO₂ and NH₃ molecules compared to classical computed results using the traditional diagonalization method.