Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex
quantum systems. One of the major goals of these approaches is to provide a reliable solution (or an accurate approximation) of the quantum
many-body problem. The diverse flavors of quantum Monte Carlo approaches all share the common use of the
Monte Carlo method to handle the multi-dimensional integrals that arise in the different formulations of the
many-body problem. The 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 and offering an exact solution of the
many-body problem in some circumstances. In particular, there exist numerically exact and
polynomially-scaling
algorithms to exactly study static properties of
boson systems without
geometrical frustration. 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.