ePrints@IIScePrints@IISc Home | About | Browse | Latest Additions | Advanced Search | Contact | Help

SPATIAL SEARCH ON GRAPHS WITH MULTIPLE TARGETS USING FLIP-FLOP QUANTUM WALK

Abhijith, J and Patel, Apoorva (2018) SPATIAL SEARCH ON GRAPHS WITH MULTIPLE TARGETS USING FLIP-FLOP QUANTUM WALK. In: QUANTUM INFORMATION & COMPUTATION, 18 (15-16). pp. 1295-1331.

Full text not available from this repository.

Abstract

We analyse the eigenvalue and eigenvector structure of the flip-flop quantum walk on regular graphs, explicitly demonstrating how it is quadratically faster than the classical random walk. Then we use it in a controlled spatial search algorithm with multiple target states, and determine the oracle complexity as a function of the spectral gap and the number of target states. The oracle complexity is optimal as a function of the graph size and the number of target states, when the spectral gap of the adjacency matrix is Theta(1). It is also optimal for spatial search on D > 4 dimensional hypercubic lattices. Otherwise it matches the best result available in the literature, with a much simpler algorithm. Our results also yield bounds on the classical hitting time of random walks on regular graphs, which may be of independent interest.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to RINTON PRESS, INC
Keywords: Adjacency matrix; Controlled search; Flip-flop quantum walk; Regular graph; Spatial search; Spectral gap
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Depositing User: Francis Jayakanth
Date Deposited: 10 Feb 2019 04:39
Last Modified: 10 Feb 2019 04:39
URI: http://eprints.iisc.ac.in/id/eprint/61371

Actions (login required)

View Item View Item