1205.1850 (Peter P. Rohde et al.)

Increasing the dimensionality of quantum walks using multiple walkers    [PDF]

Peter P. Rohde, Andreas Schreiber, Martin Stefanak, Igor Jex, Alexei Gilchrist, Christine Silberhorn

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.

View original: http://arxiv.org/abs/1205.1850