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arXiv · 1310.1428

Computational complexity of time-dependent density functional theory

J. D. Whitfield·M. -H. Yung·D. G. Tempel·S. Boixo·A. Aspuru-Guzik
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Abstract

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. Since a quantum computer can efficiently produce such time-dependent densities, we present a polynomial time quantum algorithm to generate the time-dependent Kohn-Sham potential with controllable error bounds. As a consequence, in contrast to the known intractability result for ground state density functional theory (DFT), the computation of the necessary time-dependent potentials given the initial state is in the complexity class described by bounded error quantum computation in polynomial time (BQP).

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J. D. Whitfield, M. -H. Yung, D. G. Tempel, S. Boixo, A. Aspuru-Guzik. 2013-10-05. Computational complexity of time-dependent density functional theory. https://doi.org/10.1088/1367-2630/16/8/083035

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