Geometric quantum adiabatic methods for bond dissociation energy calculation

In this work, by obtaining eigenstates and eigenvalues of a molecule's Hamiltonian under different geometry configuration, we are able to apply a quantum algorithm based on adiabatic evolution to calculate the dissociation energy of this molecule. In particular, we use the geometric quantum adiabatic evolution (GeoQAE)[1]. However, it has not been proved effective regarding molecules with more than 12 electrons. In this project, we make use of a tensor product matrix approximation[2] to GeoQAE so that adiabatic evolution can be achieved even when the Hamiltonian is gigantic. As a result, we can accurately calculate the bond dissociation energy of complex molecules.

[1] Hongye Yu, Deyu Lu, Qin Wu, and Tzu-Chieh Wei. Geometric quantum adiabatic methods for quantum chemistry, 2021.

[2] Geir Dahl, Jon Magne Leinaas, Jan Myrheim, and Eirik Ovrum. A tensor product matrix approximation problem in quantum physics. Linear Algebra and its Applications, 420(2):711–725, 2007.