In this talk I will analyze the problem of simulating quantum
many-body systems using quantum and classical computers. First, I will
argue that a quantum computer should be able to simulate all the
states that appear in Nature, whereas a classical computer may not be
able to do that. Second, I will introduce a new way of describing
states based on some techniques borrowed from the field of Quantum
Information Theory, and will show how one can build new algorithms
that extend DMRG to higher dimensions. Finally, I will show that Gibbs
states of short-range interaction Hamiltonians fulfill an area law
which can be understood in terms of the correlations existing in the
system.