Optimality of partial adiabatic search and its circuit model

Optimality of partial adiabatic search and its circuit model In this paper, we first uncover a fact that a partial adiabatic quantum search with $$O(\sqrt{N/M})$$ O ( N / M ) time complexity is in fact optimal, in which $$N$$ N is the total number of elements in an unstructured database, and $$M$$ M ( $$M\ge 1$$ M ≥ 1 ) of them are the marked ones(one) $$(N\gg M)$$ ( N ≫ M ) . We then discuss how to implement a partial adiabatic search algorithm on the quantum circuit model. From the implementing procedure on the circuit model, we can find out that the approximating steps needed are always in the same order of the time complexity of the adiabatic algorithm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Optimality of partial adiabatic search and its circuit model

, Volume 13 (8) – Jun 12, 2014
13 pages

Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-014-0770-6
Publisher site
See Article on Publisher Site

Abstract

In this paper, we first uncover a fact that a partial adiabatic quantum search with $$O(\sqrt{N/M})$$ O ( N / M ) time complexity is in fact optimal, in which $$N$$ N is the total number of elements in an unstructured database, and $$M$$ M ( $$M\ge 1$$ M ≥ 1 ) of them are the marked ones(one) $$(N\gg M)$$ ( N ≫ M ) . We then discuss how to implement a partial adiabatic search algorithm on the quantum circuit model. From the implementing procedure on the circuit model, we can find out that the approximating steps needed are always in the same order of the time complexity of the adiabatic algorithm.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jun 12, 2014

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