Computational complexity of time-dependent density functional theory
New Journal of Physics, vol. 16 (2014), pp. 083035
J D Whitfield, M-H Yung, D G Templ, S
Boixo, A Aspuru-Guzik
Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier
method for solving dynamical many-body problems in physics and chemistry. The
mathematical foundations of TDDFT are established through the formal existence of a
fictitious non-interacting system (known as the Kohn–Sham system), which can
reproduce the one-electron reduced probability density of the actual system. We
build upon these works and show that on the interior of the domain of existence,
the Kohn–Sham system can be efficiently obtained given the time-dependent density.
We introduce a V-representability parameter which diverges at the boundary of the
existence domain and serves to quantify the numerical difficulty of constructing
the Kohn–Sham potential. For bounded values of V-representability, we present a
polynomial time quantum algorithm to generate the time-dependent Kohn–Sham
potential with controllable error bounds.