One of the major goals of these approaches is to provide a reliable solution (or an accurate approximation) of the quantum many-body problem.
Quantum Monte Carlo methods allow for a direct treatment and description of complex many-body effects encoded in the wave function, going beyond mean-field theory.
For fermions, there exist very good approximations to their static properties and numerically exact exponentially scaling quantum Monte Carlo algorithms, but none that are both.
The most advanced quantum Monte Carlo approaches provide an exact solution to the many-body problem for non-frustrated interacting boson systems, while providing an approximate description of interacting fermion systems.
From a probabilistic point of view, the computation of the top eigenvalues and the corresponding ground state eigenfunctions associated with the Schrödinger equation relies on the numerical solving of Feynman–Kac path integration problems.