Geometric quantum adiabatic methods for quantum chemistry

TL;DR

This paper introduces a geometric adiabatic quantum algorithm for quantum chemistry that maintains stability and accuracy at large atomic distances by smoothly deforming molecular structures, overcoming issues like energy gap closing.

Contribution

The authors propose a novel geometric adiabatic method that improves stability and accuracy in quantum chemistry simulations, especially at large atomic distances, compared to previous approaches.

Findings

Outperforms previous methods in stability and accuracy.

Effectively handles large atomic distances and bond breaking.

Achieves high fidelity with ground states in tested examples.

Abstract

Existing quantum algorithms for quantum chemistry work well near the equilibrium geometry of molecules, but the results can become unstable when the chemical bonds are broken at large atomic distances. For any adiabatic approach, this usually leads to serious problems, such as level crossing and/or energy gap closing 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 changing bond lengths and bond angles. Even with a simple uniform stretching of chemical bonds, this algorithm performs more stably and achieves better accuracy than our previous adiabatic method [Phys. Rev. Research 3, 013104 (2021)]. It solves the problems related to energy gap closing and level crossing along the adiabatic evolution path at large atomic distances. We demonstrate its utility in several examples, including H${}_2$O, CH${}_2$, and a chemical reaction of H${}_2$+D${}_2\rightarrow$ 2HD. Furthermore, our fidelity analysis demonstrates that even with finite bond length changes, our algorithm still achieves high fidelity with the ground state.