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arXiv:quant-ph/0110098

Chen and Diao's quantum search algorithm is not exponentially fast

Chang-Cun Tu, Long, Gui Lu

Published Oct 16, 2001• 1 citation
arXivHTMLPDF

Abstract

This paper has been withdrawn due to the withdrawal of the related paper.
DOI
10.48550/arxiv.quant-ph/0110098

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A Quantum Search Algorithm for a Specified Number of Targets

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The quantum search algorithm of Chen and Diao, which finds with certainty a single target item in an unsorted database, is modified so as to be capable of searching for an arbitrary specified number of target items. If the number of targets, nu_0, is a power of four, the new algorithm will with certainty find one of the targets in a database of n items using (1/2)(3(N/nu_0)^{log_base_4(3)}-1) \approx (1/2)(3(N/nu_0)^{0.7925}-1) oracle calls, where N is the smallest power of four greater than or equal to n. If nu_0 is not a power of four, the algorithm will, with a probability of at least one-half, find one of the targets using no more than (1/2)(9(N/nu)^{log_base_4(3)}-1) calls, where nu is the smallest power of four greater than or equal to nu_0.

arXiv:quant-ph/0104082•Apr 17, 2001•0 citations
The quantum search algorithm of Chen and Diao, which finds with certainty a single target item in an unsorted database, is modified so as to be capable of searching for an arbitrary specified number of target items. If the number of targets, nu_0, is a power of four, the new algorithm will with certainty find one of the targets in a database of n items using (1/2)(3(N/nu_0)^{log_base_4(3)}-1) \approx (1/2)(3(N/nu_0)^{0.7925}-1) oracle calls, where N is the smallest power of four greater than or equal to n. If nu_0 is not a power of four, the algorithm will, with a probability of at least one-half, find one of the targets using no more than (1/2)(9(N/nu)^{log_base_4(3)}-1) calls, where nu is the smallest power of four greater than or equal to nu_0.