Different areas of quantum chemistry encounter exponential complexity of the underlying exact wave-functions. The suggested solutions are specific to each subdivision. On the other hand, recent developments in quantum computing theory prove that a general ground state search problem with two-body Hamiltonians cannot be solved in polynomial time. We suggest that a quantum chemical problem of the ground state energy search, with particles coupled via non-relativistic Coulomb operator, is also non-polynomial in time with respect to the system size. The consequences of this are explored, with an emphasis on the complexity of the quantum potential in quantum trajectory approach. (C) 2008 Elsevier B.V. All rights reserved.