Quantum Search Algorithms on Hierarchical Networks
  The "abstract search algorithm" is a well known quantum method to find a marked vertex in a graph. It has been applied with success to searching algorithms for the hypercube and the two-dimensional grid. In this work we provide an example for which that method fails to provide the best algorithm in terms of time complexity. We analyze search algorithms in degree-3 hierarchical networks using quantum walks driven by non-groverian coins. Our conclusions are based on numerical simulations, but the hierarchical structures of the graphs seems to allow analytical results. 
F. L. Marquezino, R. Portugal and S. Boettcher
quant-ph cond-mat.dis-nn