We highlight obstructions to using quantum approaches as a replacement for standard self-consistent field method solutions using simple, well-motivated examples of convergence issues. Due to multiple local minima there is no a priori guarantee that typical quantum approaches will find the global solution.

We conclude that the application of quantum technology to Hartree-Fock may serve as a hardware benchmark but is unlikely to have a serious impact on the practical approaches.

For details see "Limitations of Hartree-Fock with quantum resources", by Sahil Gulania, James Whitfield, arXiv:2007.09806.