  The ideas of digital simulation of quantum systems using a quantum computer
parallel the original ideas of numerical simulation using a classical computer.
In order for quantum computational simulations to advance to a competitive
point, many techniques from classical simulations must be imported into the
quantum domain. In this article, we consider the applications of symmetry in
the context of quantum simulation. Building upon well established machinery, we
propose a form of first quantized simulation that only requires the spatial
part of the wave function, thereby allowing spin-free quantum computational
simulations. We go further and discuss the preparation of N-body states with
specified symmetries based on projection techniques. We consider two simple
examples, molecular hydrogen and cyclopropenyl cation, to illustrate the ideas.
While the methods here represent adaptations of known quantum algorithms, they
are the first to explicitly deal with preparing N-body symmetry-adapted states.
