Abstract
Grover’s quantum search algorithm finds one of t solutions in N candidates by using (π/4)\( \sqrt {{N \mathord{\left/ {\vphantom {N t}} \right. \kern-\nulldelimiterspace} t}} \)basic steps. It is, however, necessary to know the number t of solutions in advance for using the Grover’s algorithm directly. On the other hand, Boyer etal proposed a randomized application of Grover’s algorithm, which runs, on average, in Oi(\( \sqrt {{N \mathord{\left/ {\vphantom {N t}} \right. \kern-\nulldelimiterspace} t}} \)) basic steps (more precisely, (9/4)\( \sqrt {{N \mathord{\left/ {\vphantom {N t}} \right. \kern-\nulldelimiterspace} t}} \) steps) without knowing t in advance. Here we show a simple (almost trivial) deterministic application of Grover’s algorithm also works and finds a solution in O \( \sqrt {{N \mathord{\left/ {\vphantom {N t}} \right. \kern-\nulldelimiterspace} t}} \)) basic steps (more precisely, (8π/3)\( \sqrt {{N \mathord{\left/ {\vphantom {N t}} \right. \kern-\nulldelimiterspace} t}} \) steps) on average.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
E. Bernstein and U. Vazirani, Quantum complexity theory, SIAM Journal on Computing 26, 1411–1473 (1997).
M. Boyer, G. Brassard, P. Hoyer, and A. Tapp, Tight bounds on quantum searching, quant-ph/9605034.
L. Fortnow, One complexity theorist’s view of quantum computing, quant-ph/0003035.
L.K. Grover, A fastquantum mechanical algorithm for database search,in Proc. 28th Annual ACM Symposium on Theory of Computing, ACM, 212–219 (1996).
L.K. Grover, Quantum mechanics helps in searching for a needle in a haystack, Phys.Rev.Lett 79, 325–328 (1997).
J. Gruska, Quantum Computing, McGrow-Hill, 1999.
A. Hosoya, Lectures on Quantum Computation (in Japanese), Science Pub. Co., 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Okamoto, K., Watanabe, O. (2001). Deterministic Application of Grover’s Quantum Search Algorithm. In: Wang, J. (eds) Computing and Combinatorics. COCOON 2001. Lecture Notes in Computer Science, vol 2108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44679-6_55
Download citation
DOI: https://doi.org/10.1007/3-540-44679-6_55
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42494-9
Online ISBN: 978-3-540-44679-8
eBook Packages: Springer Book Archive