Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer

TL;DR

This paper presents a method to derive exact density functionals and Kohn-Sham potentials using a quantum computer, enabling efficient solutions for quantum chemical systems with machine learning techniques.

Contribution

It introduces a novel approach combining quantum algorithms and machine learning to obtain exact functionals, reducing the need for wavefunction re-preparation and enabling classical self-consistent solutions.

Findings

Quantum algorithms can efficiently learn exact density functionals.

Finding Kohn-Sham potentials is not more difficult than obtaining ground state densities.

Classical models can use the learned functionals for self-consistent ground state calculations.

Abstract

One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory. We demonstrate a general method for obtaining the exact functional as a machine learned model from a sufficiently powerful quantum computer. Only existing assumptions for the current feasibility of solutions on the quantum computer are used. Several known algorithms including quantum phase estimation, quantum amplitude estimation, and quantum gradient methods are used to train a machine learned model. One advantage of this combination of algorithms is that the quantum wavefunction does not need to be completely re-prepared at each step, lowering a sizable pre-factor. Using the assumptions for solutions of the ground-state algorithms on a quantum computer, we demonstrate that finding the Kohn-Sham potential is not necessarily more difficult than the ground state density. Once constructed, a classical user can use the resulting machine learned functional to solve for the ground state of a system self-consistently, provided the machine learned approximation is accurate enough for the input system. It is also demonstrated how the classical user can access commonly used time- and temperature-dependent approximations from the ground state model. Minor modifications to the algorithm can learn other types of functional theories including exact time- and temperature-dependence. Several other algorithms--including quantum machine learning--are demonstrated to be impractical in the general case for this problem.