  This paper is an introduction to diagrammatic methods for representing
quantum processes and quantum computing. We review basic notions for quantum
information and quantum computing. We discuss topological diagrams and some
issues about using category theory in representing quantum computing and
teleportation. We analyze very carefully the diagrammatic meaning of the usual
representation of the Mach-Zehnder interferometer, and we show how it can be
generalized to associate to each composition of unitary transformations a
"laboratory quantum diagram" such that particles moving though the many
alternate paths in this diagram will mimic the quantum process represented by
the composition of unitary transformations. This is a finite dimensional way to
think about the Feynman Path Integral. We call our representation result the
Path Theorem. Then we go back to the basics of networks and matrices and show
how elements of quantum measurement can be represented with network diagrams.
