Electronic Structure Calculations and the Ising Hamiltonian

The exact solution of the Schrodinger equation for atoms, molecules and extended systems continues to be a "Holy Grail" problem for the field of atomic and molecular physics since inception. Recently, breakthroughs have been made in the development of hardware- efficient quantum optimizers and coherent Ising machines capable of simulating hundreds of interacting spins through an Ising-type Hamiltonian. One of the most vital questions associated with these new devices is: "Can these machines be used to perform electronic structure calculations?" In this study, we discuss the general standard procedure used by these devices and show that there is an exact mapping between the electronic structure Hamiltonian and the Ising Hamiltonian. The simulation results of the transformed Ising Hamiltonian for H2, He2, HeH+, and LiH molecules match the exact numerical calculations. This demonstrates that one can map the molecular Hamiltonian to an Ising-type Hamiltonian which could easily be implemented on currently available quantum hardware.

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