Spatial search on graphs with multiple targets using flip-flop quantum walk

Abhijith, J and Patel, A (2018) Spatial search on graphs with multiple targets using flip-flop quantum walk. In: Quantum Information and Computation, 18 (15-16). pp. 1295-1331.

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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 Θ(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
Publication:	Quantum Information and Computation
Publisher:	Rinton Press Inc.
Additional Information:	The copyright for this article belongs to Rinton Press Inc.
Keywords:	Eigenvalues and eigenfunctions; Graph structures; Graph theory; Matrix algebra; Random processes, Adjacency matrices; Controlled search; Quantum walk; Regular graphs; Spatial search; Spectral gap, Flip flop circuits
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	04 Aug 2022 06:18
Last Modified:	04 Aug 2022 06:18
URI:	https://eprints.iisc.ac.in/id/eprint/75118

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