# Electronic Structure Calculations and the Ising Hamiltonian

## TL;DR

This paper demonstrates that electronic structure Hamiltonians can be exactly mapped to Ising Hamiltonians, enabling the use of quantum Ising machines for molecular simulations with results matching exact calculations.

## Contribution

It introduces an exact mapping procedure from electronic structure Hamiltonians to Ising Hamiltonians for quantum hardware implementation.

## Key findings

- Simulation results for H2, He2, HeH+, and LiH match exact calculations.
- The mapping enables use of current quantum hardware for electronic structure problems.
- Supports the potential of quantum Ising machines in quantum chemistry.

## Abstract

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.