Geometric quantum adiabatic path for molecular eigensystems

We propose a quantum algorithm based on adiabatic evolution  to obtain molecular eigen-states and eigen-energies, which exploits slow stretching of bonding lengths and possibly angles. We refer to this scheme as geometric quantum adiabatic evolution (GeoQAE). In a previous work, we used a Hamiltonian path connecting to the final molecular Hamiltonian from the associated maximally commuting one, but this Mc-QAE approach encounters small energy gaps and level crossing at large molecular distances. Our new GeoQAE approach solves this problem and we  simulate the quantum evolution and the final energy in several examples, including H₂O, CH₂, and a chemical reaction study on H₂+D₂ →2HD.