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Search on a fractal lattice using a quantum random walk

Patel, Apoorva and Raghunathan, KS (2012) Search on a fractal lattice using a quantum random walk. In: PHYSICAL REVIEW A, 86 (1).

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Official URL: http://dx.doi.org/10.1103/PhysRevA.86.012332

Abstract

The spatial search problem on regular lattice structures in integer number of dimensions d >= 2 has been studied extensively, using both coined and coinless quantum walks. The relativistic Dirac operator has been a crucial ingredient in these studies. Here, we investigate the spatial search problem on fractals of noninteger dimensions. Although the Dirac operator cannot be defined on a fractal, we construct the quantum walk on a fractal using the flip-flop operator that incorporates a Klein-Gordon mode. We find that the scaling behavior of the spatial search is determined by the spectral (and not the fractal) dimension. Our numerical results have been obtained on the well-known Sierpinski gaskets in two and three dimensions.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to American Physical Society
Department/Centre: Division of Information Sciences > Supercomputer Education & Research Centre
Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 10 Sep 2012 12:21
Last Modified: 10 Sep 2012 12:21
URI: http://eprints.iisc.ernet.in/id/eprint/45001

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