  We report our research on disordered complex systems using cold gases and
trapped ions, and address the possibility of using complex systems for quantum
information processing. Two simple paradigmatic models of disordered complex
systems are revisited here. The first one corresponds to a short range
disordered Ising Hamiltonian (spin glasses), which can be implemented with a
Bose-Fermi (Bose-Bose) mixture in a disordered optical lattice. The second
model we address here is a long range disordered Hamiltonian, characteristic of
neural networks (Hopfield model), which can be implemented in a chain of
trapped ions with appropriately designed interactions.
