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

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