  Quantum Chemistry and Physics have been pinpointed as killer applications for
quantum computers, and quantum algorithms have been designed to solve the
Schr\"odinger equation with the wavefunction formalism. It is yet limited to
small systems, as their size is limited by the number of qubits available.
Computations on large systems rely mainly on mean-field-type approaches such as
density functional theory, for which no quantum advantage has been envisioned
so far. In this work, we question this a priori by proposing a
counter-intuitive mapping from the non-interacting to an auxiliary interacting
Hamiltonian that may provide the desired advantage.
