Increasing the dimensionality of quantum walks using multiple walkers

Publication Type:
Journal Article
Journal of Computational and Theoretical Nanoscience, 2013, 10 (7), pp. 1644 - 1652
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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 and 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. Copyright © 2013 American Scientific Publishers.
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