  We show that with the addition of multiple walkers, quantum walks on a line
can be transformed into lattice graphs of higher dimension. Thus, multi-walker
walks can simulate single-walker walks on higher dimensional graphs and vice
versa. This exponential complexity opens up new applications for present-day
quantum walk experiments. We discuss the applications of such
higher-dimensional structures and how they relate to linear optics quantum
computing. In particular we show that multi-walker quantum walks are equivalent
to the BosonSampling model for linear optics quantum computation proposed by
Aaronson & Arkhipov. With the addition of control over phase-defects in the
lattice, which can be simulated with entangling gates, asymmetric lattice
structures can be constructed which are universal for quantum computation.
