A new quantum claw-finding algorithm for three functions

Authors:
Kazuo Iwama;Akinori Kawachi
Affiliations:
Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606-8501, Japan, Quantum Computation and Information Project, ERATO, JST 406, Iseya-cho, Kamigyo-ku, Kyoto 602-0 ...;Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606-8501, Japan, Quantum Computation and Information Project, ERATO, JST 406, Iseya-cho, Kamigyo-ku, Kyoto 602-0 ...
Venue:
New Generation Computing - Quantum computing
Year:
2003

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Abstract

For k functions f1,...,fk, a k-tuple (x1,...,xk) such that f1(x1) = ... = fk(xk) is called a claw of f1,...,fk. In this paper, we construct a new quantum claw-finding algorithm for three functions that is efficient when the number M of intermediate solutions is small. The known quantum claw-finding algorithm for three functions requires O(N7/8 log N) queries to find a claw, but our algorithm requires O(N3/4 log N) queries if M ≤ √N and O(N7/12M1/3 log N) queries otherwise. Thus, our algorithm is more efficient if M ≤ N7/8.