Guifré Vidal, then at the Institute for Quantum Information, Caltech, has recently proposed a scheme useful for simulating a certain category of quantum systems. He asserts that "any quantum computation with pure states can be efficiently simulated with a classical computer provided the amount of entanglement involved is sufficiently restricted". This happens to be the case with generic Hamiltonians displaying local interactions, as for example, Hubbard -like Hamiltonians. The method exhibits a low-degree polynomial behavior in the increase of computational time with respect to the amount of entanglement present in the system. The algorithm is based on a scheme that exploits the fact that in these one-dimensional systems the eigenvalues of the reduced density matrix on a bipartite split of the system are exponentially decaying, thus allowing us to work in a re-sized space spanned by the eigenvectors corresponding to the eigenvalues we selected.