pioneering paper [@Grover] Grover presented a quantum algorithm that can be used to search an unsorted database quadratically faster than the existing classical algorithms. Shenvi, Kempe and Whaley (SKW) [@shenvi:052307] proposed a search algorithm based on quantum random walk on a hypercube, which has similar scaling properties as the Grover search. In the SKW algorithm the oracle is used to modify the quantum coin at the marked vertex. In contrast to the Grover search, this algorithm generally has to be repeated several times to produce a result, but this merely adds a fixed overhead independent of the size of the search space.

There are various suggestions and some experiments how to realize quantum walks in a laboratory. The schemes proposed specifically for the implementation of QRWs include ion traps [@travaglione:032310], nuclear magnetic resonance [@du-2003-67] (also experimentally verified [@Ryan2005Experimental-im]), cavity quantum electrodynamics [@di:032304; @agarwal:033815], optical lattices [@dur-2002-66], optical traps [@eckert:012327], optical cavity [@Roldan2005Optical-impleme], and classical optics [@knight-2003-227]. Moreover, the application of standard general logic networks to the task is always at hand [@Hines-pra75; @Fujiwara2005Scalable-networ].

The idea of the scattering quantum random walk (SQRW) [@hillery:032314] was proposed as an answer to the question that can be posed as: how to realize a 