  We calculate the amount of entanglement of the multiqubit quantum states
employed in the Grover algorithm, by following its dynamics at each step of the
computation. We show that genuine multipartite entanglement is always present.
Remarkably, the dynamics of any type of entanglement as well as of genuine
multipartite entanglement is independent of the number n of qubits for large n,
thus exhibiting a scale invariance property. We compare this result with the
entanglement dynamics induced by a fixed-point quantum search algorithm. We
also investigate criteria for efficient simulatability in the context of
Grover's algorithm.
