Search on a hypercubic lattice using a quantum random walk. I. d > 2

Patel, Apoorva D and Rahaman, Md Aminoor (2010) Search on a hypercubic lattice using a quantum random walk. I. d > 2. In: Physical Review A, 82 (3).

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Abstract

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d > 2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d -> infinity limit). In particular, the scaling behavior for d = 3 is only about 25% higher than the optimal d -> infinity value.

Item Type:	Journal Article
Publication:	Physical Review A
Publisher:	The American Physical Society
Additional Information:	Copyright of this article belongs to The American Physical Society.
Department/Centre:	Division of Interdisciplinary Sciences > Supercomputer Education & Research Centre Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	21 Oct 2010 05:11
Last Modified:	21 Oct 2010 05:11
URI:	http://eprints.iisc.ac.in/id/eprint/33266

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