  We study quantum algorithms for spatial search on finite dimensional grids.
Patel et al. and Falk have proposed algorithms based on a quantum walk without
a coin, with different operators applied at even and odd steps. Until now, such
algorithms have been studied only using numerical simulations. In this paper,
we present the first rigorous analysis for an algorithm of this type, showing
that the optimal number of steps is $O(\sqrt{N\log N})$ and the success
probability is $O(1/\log N)$, where $N$ is the number of vertices. This matches
the performance achieved by algorithms that use other forms of quantum walks.
