Density functionals and KohnSham potentials with minimal wavefunction preparations on a quantum computer
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 reprepared at each step, lowering a sizable prefactor. Using the assumptions for solutions of the groundstate algorithms on a quantum computer, we demonstrate that finding the KohnSham potential is not necessarily more difficult than the groundstate density. Once constructed, a classical user can use the resulting machine learned functional to solve for the ground state of a system selfconsistently, 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 temperaturedependent approximations from the groundstate 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.
 Publication:

Physical Review Research
 Pub Date:
 November 2020
 DOI:
 10.1103/PhysRevResearch.2.043238
 arXiv:
 arXiv:2008.05592
 Bibcode:
 2020PhRvR...2d3238B
 Keywords:

 Quantum Physics;
 Condensed Matter  Other Condensed Matter
 EPrint:
 27 pages, 4 figures