# Electronic structure calculations and the Ising model: practical?

I was reading this paper which introduces a mapping from a qubit Hamiltonian to an Ising model. Firstly, the first step of the mapping seems to assume that we know an eigenstate of the system (correct me here because it seems unlikely in practice). Below, is the mention of the first step :

Secondly, such mapping seems extremely costly if we look at their complexity.

My question is: would this method be considered interesting for practice compared to classical methods and how can this be implemented on practical examples?

• What is meant by "Classical Methods" later in your question? – Siddhant Singh Nov 4 '18 at 14:56
• Any classical method/algorithms that people in the field use for such purpose. – cnada Nov 4 '18 at 15:00

The electronic structure Hamiltonian after the Jordan-Wigner or Bravyi-Kitaev transformation (which the authors of this paper did use) has quadratic (and sometimes higher-order) terms containing $$\sigma_x, \sigma_y$$, and $$\sigma_z$$, but the Ising model does not have any quadratic terms containing $$\sigma_x$$ in any way.
It is possible to efficiently simulate any Hamiltonian using a Hamiltonian that has quadratic terms containing $$\sigma_x$$, as proven by Biamonte & Love. However, since the Ising Hamiltonian does not have such terms, which are required to simulate the electronic structure Hamiltonian efficiently, the method in the paper you mentioned, is not capable of efficiently finding the ground state of the electronic structure Hamiltonian.