  In this survey paper we give an intuitive treatment of the discrete time
quantization of classical Markov chains. Grover search and the quantum walk
based search algorithms of Ambainis, Szegedy and Magniez et al. will be stated
as quantum analogues of classical search procedures. We present a rather
detailed description of a somewhat simplified version of the MNRS algorithm.
Finally, in the query complexity model, we show how quantum walks can be
applied to the following search problems: Element Distinctness, Matrix Product
Verification, Restricted Range Associativity, Triangle, and Group
Commutativity.
