  Quantum walks have emerged as an interesting alternative to the usual circuit
model for quantum computing. While still universal for quantum computing, the
quantum walk model has very different physical requirements, which lends itself
more naturally to some physical implementations, such as linear optics.
Numerous authors have considered walks with one or two walkers, on one
dimensional graphs, and several experimental demonstrations have been
performed. In this paper we discuss generalizing the model of discrete time
quantum walks to the case of an arbitrary number of walkers acting on arbitrary
graph structures. We present a formalism which allows for analysis of such
situations, and several example scenarios for how our techniques can be
applied. We consider the most important features of quantum walks --
measurement, distinguishability, characterization, and the distinction between
classical and quantum interference. We also discuss the potential for physical
implementation in the context of linear optics, which is of relevance to
present day experiments.
