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- W202268132 abstract "We show how to extract the scaling behavior of quantum walks using renormalization. We introduce the method by efficiently reproducing well-known results on the one-dimensional lattice. We argue that an extended interpretation of the traditional renormalization group formalism is required to obtain scaling exponents. Applied to the dual Sierpinski gasket as a nontrivial model that lacks translational invariance, our treatment of the quantum walk reveals an immensely rich phenomenology for its spreading. Invariably, quantum interference localizes the walk completely with a site-access probability that declines with a powerlaw from the initial site, where a classical random walk would pass all sites with certainty. Nonetheless, we find that under rescaling the system length, $L^{prime}=2L$, characteristic times rescale as $t^{prime}=2^{d_{w}}t$ with the walk exponent $d_{w}=log_{2}sqrt{5}=1.1609ldots$, very close to the ballistic spreading, $d_{w}=1$, found for regular lattices. This improves the prospect of applying quantum search algorithms to unstructured databases such as the internet." @default.
- W202268132 created "2016-06-24" @default.
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- W202268132 date "2013-11-14" @default.
- W202268132 modified "2023-09-23" @default.
- W202268132 title "Quantum Walks and Interference without Translational Invariance" @default.
- W202268132 hasPublicationYear "2013" @default.
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