Quantum simulation and Time-Dependent Density Functional Theory

Time evolution of quantum systems is of interest in physics, in chemistry, and, more recently, in computer science. One route to numerically propagating quantum systems is time dependent density functional theory. The application of TDDFT to a particular system's time evolution is predicated on V-representablility which we've analyzed in previous work. Here we consider the application of quantum simulation to the problem of characterizing time-dependent Kohn-Sham potentials. We consider both the V-representability of some simple 1D examples numerically and their implementation using quantum computation. The measurement of the one-body electronic probability density on quantum hardware given various qubit encodings is also discussed.