  We propose the use of quantum optical systems to perform universal simulation
of quantum dynamics. Two specific implementations that require present
technology are put forward for illustrative purposes. The first scheme consists
of neutral atoms stored in optical lattices, while the second scheme consists
of ions stored in an array of micro--traps. Each atom (ion) supports a
two--level system, on which local unitary operations can be performed through a
laser beam. A raw interaction between neighboring two--level systems is
achieved by conditionally displacing the corresponding atoms (ions). Then,
average Hamiltonian techniques are used to achieve evolutions in time according
to a large class of Hamiltonians.
