  In this paper, we study the quantum walk on the 2D Penrose Lattice, which is
intermediate between periodic and disordered structure. Quantum walk on Penrose
Lattice is less efficient in transport comparing to the regular lattices. By
calculating the final remaining probability on the initial nodes and estimating
the low bound. Our results show that the broken of translational symmetry
induces both the localized states and degeneracy of eigenstates at $E=0$, this
two differences from regular lattices influence efficiency of quantum walk.
Also, we observe the transition from inefficient to efficient transport after
introducing the near hopping terms, which suggests that we can adjust the
"hopping strength" and achieve a "phase transition" progress.
