  It is shown that a particular class of so-called strongly frustration-free
many-body Hamiltonians can be Monte Carlo simulated efficiently on a classical
computing machine, because the ground state of such a Hamiltonian is locally
determined in the sense of having a nodal structure that is efficiently
computable locally by solving a small subsystem associated with a
low-dimensional configuration subspace. It is further demonstrated that
strongly frustration-free Hamiltonians can be designed to implement universal
ground state quantum computation. The two results combined have effectively
solved the notorious sign problem in Monte Carlo simulations, and proved that
all bounded-error quantum polynomial time algorithms admit bounded-error
probabilistic polynomial time simulations.
