Geometric quantum adiabatic methods for quantum chemistry

Abstract

Quantum algorithms have been successfully applied in quantum chemistry to obtain the ground-state energy of small molecules. Although accurate near the equilibrium geometry, the results can become unreliable when the chemical bonds are broken at large distances. For any adiabatic approach, this is usually caused by serious issues, such as energy gap closing or level crossing along the adiabatic evolution path. In this work, we propose a quantum algorithm based on adiabatic evolution to obtain molecular eigenstates and eigenenergies in quantum chemistry, which exploits a smooth geometric deformation by continuously varying bond lengths and bond angles. We demonstrate its utility in several examples on a noiseless quantum simulator, including H_{2}O, CH_{2}, and a chemical reaction of H_{2}+D_{2}→ 2HD, by uniformly stretching chemical bonds. We find that this new algorithm solves the problems related to energy gap closing and level crossing along the adiabatic evolution path at large atomic distances. The new method performs more stably and achieves better accuracy than our previous adiabatic method [Yu and Wei, Phys. Rev. Research 3, 013104 (2021)]2643-156410.1103/PhysRevResearch.3.013104. Furthermore, our fidelity analysis demonstrates that even with finite bond length changes, our algorithm still achieves high fidelity for the ground state.