We have shown the electronic structure problem is QMA-hard without magnetic field but restricted to a fixed orbital basis.

Our main result shows consider electronic structure Hamiltonians restricted to a fixed number of electrons and projected into a fixed single-particle basis. We conclusively demonstrate that these properties do not add enough structure to enable the existence of an efficient quantum simulation algorithm to approximate the ground state energy of such systems.

For details see

“Electronic Structure in a Fixed Basis is QMA-complete”, B. O’Gorman, S. Irani,** **J. Whitfield, B. Fefferman. arXiv:2103.08215