  The quantum walk was originally proposed as a quantum mechanical analogue of
the classical random walk, and has since become a powerful tool in quantum
information science. In this paper, we show that discrete time quantum walks
provide a versatile platform for studying topological phases, which are
currently the subject of intense theoretical and experimental investigation. In
particular, we demonstrate that recent experimental realizations of quantum
walks simulate a non-trivial one dimensional topological phase. With simple
modifications, the quantum walk can be engineered to realize all of the
topological phases which have been classified in one and two dimensions. We
further discuss the existence of robust edge modes at phase boundaries, which
provide experimental signatures for the non-trivial topological character of
the system.

Mesoscale and Nanoscale Physics;Quantum Physics