Toward density functional theory on quantum computers?

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