  Quantum random walks on graphs have been shown to display many interesting
properties, including exponentially fast hitting times when compared with their
classical counterparts. However, it is still unclear how to use these novel
properties to gain an algorithmic speed-up over classical algorithms. In this
paper, we present a quantum search algorithm based on the quantum random walk
architecture that provides such a speed-up. It will be shown that this
algorithm performs an oracle search on a database of $N$ items with
$O(\sqrt{N})$ calls to the oracle, yielding a speed-up similar to other quantum
search algorithms. It appears that the quantum random walk formulation has
considerable flexibility, presenting interesting opportunities for development
of other, possibly novel quantum algorithms.
