  We show how a quantum computer may efficiently simulate a disordered
Hamiltonian, by incorporating a pseudo-random number generator directly into
the time evolution circuit. This technique is applied to quantum simulation of
few-body disordered systems in the large volume limit; in particular, Anderson
localization. The method requires a number of (error corrected) qubits
proportional to the logarithm of the volume of the system, and each time
evolution step requires a number of gates polylogarithmic in the volume. We
simulate the method to observe the metal-insulator transition on a
three-dimensional lattice. Additionally, we demonstrate the algorithm on a
one-dimensional lattice, using physical quantum processors.
