Quantum computational complexity of time-dependent density functional theory

J. D. Whitfield

VCQ Postdoctoral Fellow
Vienna Center for Quantum Science and Technology

Abstract

Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving problems of many-body dynamics in physics and chemistry. Recent investigations into the mathematical foundations of TDDFT have investigated the formal existence of a non-interacting system (Kohn-Sham system) which can reproduce the density of the actual system. Here we build upon these works and show that on the interior of the domain where such a system exists, it can be efficiently obtained given the time-dependent density. Since a quantum computer can produce and be simulated by such time-dependent densities, we find that the computational power of TDDFT using a Kohn-Sham system is essentially that of a quantum computer. Our results are also complementary to a previous result showing that ground-state problems solvable by density function theory are hard problems even for a quantum computer. Remarkably, this is a result in contrast with computational physics in practice where the conclusion is reversed, as TDDFT calculations are often more difficult than DFT. Therefore, our findings provide more reasons why quantum computers should be built.