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Quantum walks have emerged as an interesting alternative to the usual circuitmodel for quantum computing. While still universal for quantum computing, thequantum walk model has very different physical requirements, which lends itselfmore naturally to some physical implementations, such as linear optics.Numerous authors have considered walks with one or two walkers, on onedimensional graphs, and several experimental demonstrations have beenperformed. In this paper we discuss generalizing the model of discrete timequantum walks to the case of an arbitrary number of walkers acting on arbitrarygraph structures. We present a formalism which allows for analysis of suchsituations, and several example scenarios for how our techniques can beapplied. We consider the most important features of quantum walks --measurement, distinguishability, characterization, and the distinction betweenclassical and quantum interference. We also discuss the potential for physicalimplementation in the context of linear optics, which is of relevance topresent day experiments.

Multi-walker discrete time quantum walks on arbitrary graphs, their properties, and their photonic implementation