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 |
|---|---|
| Publication: | QUANTUM INFORMATION & COMPUTATION |
| Publisher: | RINTON PRESS, INC |
| 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 |
| Date Deposited: | 10 Feb 2019 04:39 |
| Last Modified: | 10 Feb 2019 04:39 |
| URI: | http://eprints.iisc.ac.in/id/eprint/61371 |
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