Geometric quantum adiabatic methods for quantum chemistry

• URL: http://arxiv.org/abs/2112.15186v1
• Date: Thu, 30 Dec 2021 19:31:29 GMT
• Title: Geometric quantum adiabatic methods for quantum chemistry
• Authors: Hongye Yu, Deyu Lu, Qin Wu, Tzu-Chieh Wei
• Abstract summary: We propose a quantum algorithm based on adiabatic evolution to obtain molecular eigenstates and eigenenergies in quantum chemistry. Our algorithm exploits a smooth geometric deformation by changing bond lengths and bond angles. It solves the problems related to energy gap closing and level crossing along the adiabatic evolution path at large atomic distances.
• Score: 0.6554326244334867
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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