Computational complexity in electronic structure

James Daniel Whitfield, Peter John Love, Alán Aspuru-Guzik
2013 Physical Chemistry, Chemical Physics - PCCP  
In quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere shortcomings of the algorithm designers and programmers but could stem from the inherent difficulty of simulating quantum systems. Extensions of computer science and information processing exploiting quantum mechanics has led to new ways of understanding the ultimate
more » ... imitations of computational power. Interestingly, this perspective helps us understand widely used model chemistries in a new light. In this article, the fundamentals of computational complexity will be reviewed and motivated from the vantage point of chemistry. Then recent results from the computational complexity literature regarding common model chemistries including Hartree-Fock and density functional theory are discussed.
doi:10.1039/c2cp42695a pmid:23172634 fatcat:zqscceg3qbeavgo5ogimzdtrxe