  We present an algorithm that exploits quantum parallelism to simulate
randomness in a quantum system. In our scheme, all possible realizations of the
random parameters are encoded quantum mechanically in a superposition state of
an auxiliary system. We show how our algorithm allows for the efficient
simulation of dynamics of quantum random spin chains with known numerical
methods. We also propose an experimental realization based on atoms in optical
lattices in which disorder could be simulated in parallel and in a controlled
way through the interaction with another atomic species.
