  The Hartree-Fock problem provides the conceptual and mathematical
underpinning of a large portion of quantum chemistry. As efforts in quantum
technology aim to enhance computational chemistry algorithms, the fundamental
Hartree-Fock problem is a natural target. While quantum computers and quantum
simulation offer many prospects for the future of modern chemistry, the
Hartree-Fock problem is not a likely candidate. We highlight this fact from a
number of perspectives including computational complexity, practical examples,
and the full characterization of the energy landscapes for simple systems.
