Deterministic quantum search with adjustable parameters: Implementations and applications

Grover's algorithm provides a quadratic speedup over classical algorithms to search for marked elements in an unstructured database. The original algorithm is probabilistic, and there are several schemes to achieve the deterministic version, by using the generalized Grover's iteration G(α,...

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Bibliographic Details
Published in:	Information and computation Vol. 292; p. 105042
Main Authors:	Li, Guanzhong, Li, Lvzhou
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.06.2023
Subjects:	Deterministic quantum algorithm Exact quantum algorithm Grover's algorithm Quantum algorithm Quantum walk search Quantum algorithm Quantum walk search Grover's algorithm Exact quantum algorithm Deterministic quantum algorithm
ISSN:	0890-5401, 1090-2651
Online Access:	Get full text
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Summary:	Grover's algorithm provides a quadratic speedup over classical algorithms to search for marked elements in an unstructured database. The original algorithm is probabilistic, and there are several schemes to achieve the deterministic version, by using the generalized Grover's iteration G(α,β):=Sr(β)So(α). However, in all the existing schemes the value range of α and β is limited; for instance, in the three early schemes they are determined by the proportion of marked states M/N. In this paper, we break through this limitation by presenting a search framework with adjustable parameters, which allows α or β to be arbitrarily given. The significance of the framework lies not only in the expansion of mathematical form, but also in its application value, as we present two disparate problems which we are able to solve deterministically using the proposed framework, whereas previous schemes are ineffective.
ISSN:	0890-5401 1090-2651
DOI:	10.1016/j.ic.2023.105042