  A general class of discrete unitary models are described whose behavior in
the continuum limit corresponds to a many-body Schrodinger equation. On a
quantum computer, these models could be used to simulate quantum many-body
systems with an exponential speedup over analogous simulations on classical
computers. On a classical computer, these models give an explicitly unitary and
local prescription for discretizing the Schrodinger equation. It is shown that
models of this type can be constructed for an arbitrary number of particles
moving in an arbitrary number of dimensions with an arbitrary interparticle
interaction.
