  We present a scheme to efficiently simulate, with a classical computer, the
dynamics of multipartite quantum systems on which the amount of entanglement
(or of correlations in the case of mixed-state dynamics) is conveniently
restricted. The evolution of a pure state of n qubits can be simulated by using
computational resources that grow linearly in n and exponentially in the
entanglement. We show that a pure-state quantum computation can only yield an
exponential speed-up with respect to classical computations if the entanglement
increases with the size n of the computation, and gives a lower bound on the
required growth.
