  Algorithms are described for efficiently simulating quantum mechanical
systems on quantum computers. A class of algorithms for simulating the
Schrodinger equation for interacting many-body systems are presented in some
detail. These algorithms would make it possible to simulate nonrelativistic
quantum systems on a quantum computer with an exponential speedup compared to
simulations on classical computers. Issues involved in simulating relativistic
systems of Dirac and gauge particles are discussed.
