Relation between fermionic and qubit mean fields in the electronic structure problem

TL;DR

This paper investigates the relationship between fermionic and qubit mean-field methods in electronic structure calculations, revealing conditions under which their energies agree or differ, especially in correlated systems.

Contribution

It establishes criteria for when fermionic and qubit mean fields yield similar or different energies, highlighting the impact of orbital choices and correlation effects.

Findings

Fermionic and qubit mean fields can differ in energy depending on orbital choices.

In weakly correlated systems, mean-field energies tend to agree.

Strong correlation can lead to symmetry breaking and lower qubit mean-field energies.

Abstract

For quantum computing applications, the electronic Hamiltonian for the electronic structure problem needs to be unitarily transformed to a qubit form. We found that mean-field procedures on the original electronic Hamiltonian and on its transformed qubit counterpart can give different results. We establish conditions of when fermionic and qubit mean fields provide the same or different energies. In cases when the fermionic mean-field (Hartree-Fock) approach provides an accurate description (electronic correlation effects are small), the choice of molecular orbitals for the electron Hamiltonian representation becomes the determining factor in whether the qubit mean-field energy will be equal to or higher than that of the fermionic counterpart. In strongly correlated cases, the qubit mean-field approach has a higher chance to undergo symmetry breaking and lower its energy below the fermionic counterpart.