# Trapping and spreading properties of quantum walk in homological structure

@article{Machida2015TrappingAS, title={Trapping and spreading properties of quantum walk in homological structure}, author={T. Machida and E. Segawa}, journal={Quantum Information Processing}, year={2015}, volume={14}, pages={1539-1558} }

We attempt to extract a homological structure of two kinds of graphs by the Grover walk. The first one consists of a cycle and two semi-infinite lines, and the second one is assembled by a periodic embedding of the cycles in $$\mathbb {Z}$$Z. We show that both of them have essentially the same eigenvalues induced by the existence of cycles in the infinite graphs. The eigenspace of the homological structure appears as so called localization in the Grover walks, in which the walk is partially… CONTINUE READING

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