Continuous Quantum Walk on Penrose Lattice
Y. M. Min, K.Wang · arXiv (Cornell University) · 2016
Transport properties play a key role in several fields of science, for example physics, biology, chemistry, sociology and information science. The behavior of many dynamical processes running over complex networks is known to be related to the underlying topology. 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 comparing to the regular lattices. By calculating the final remaining probability on the initial nodes and estimating the low bound, our results show that both the localized states and degeneracy of eigenstates at $E=0$ influence efficiency of quantum walk. Also, we observe the from inefficient to efficient transport after introducing the near terms, which suggests that we can tune the hopping strength and achieve a phase transition progress. These results might pave the way for performing universal quantum computation.