Toward Density Functional Theory on Quantum Computers?

TL;DR

This paper explores the potential for quantum computers to enhance density functional theory calculations, proposing a novel mapping that could enable quantum advantage for larger systems.

Contribution

It introduces a new mapping from non-interacting to interacting Hamiltonians, challenging the assumption that quantum advantage is limited to wavefunction methods.

Findings

Proposes a counter-intuitive Hamiltonian mapping

Suggests potential quantum advantage for DFT calculations

Challenges existing limitations of quantum algorithms for large systems

Abstract

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.