Hein, Birgit and Tanner, Gregor (2010) Quantum search algorithms on a regular lattice. PHYSICAL REVIEW A, 82 (1): 012326. ISSN 1050-2947,
Full text not available from this repository.Abstract
Quantum algorithms for searching for one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behavior for the search time and the localization probability in the limit of large lattice size including the leading order coefficients. For d = 2 and d = 3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | RANDOM-WALKS; SPECTRAL STATISTICS; GRAPHS; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Jul 2020 06:56 |
| Last Modified: | 22 Jul 2020 06:56 |
| URI: | https://pred.uni-regensburg.de/id/eprint/24452 |
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