Lower bounds of a quantum search for an extreme point
نویسندگان
چکیده
منابع مشابه
Lower bounds of Quantum Search for Extreme Point
We show that Durr-Hoyer’s quantum algorithm of searching for extreme point of integer function can not be sped up for functions chosen randomly. Any other algorithm acting in substantially shorter time o( √ 2n) (n −→ ∞) gives incorrect answer for the functions φ with the single point of maximum chosen randomly with probability Perror −→ 1. The lower bound as Ω( √ 2n/b) is established for the qu...
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Let φ be some integer function on words of length n and oracle Oφ gives the value φ(x) for a given x. It is shown how quantum algorithm can find a point of maximum of φ with the probability of error 2/3 applying oracle Oφ 32 √ 2n times. This algorithm is optimal in within constant factor in the following sense. Any other algorithm acting in substantially shorter time o( √ 2n) (n −→ ∞) gives inc...
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We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T ∈ O( √ N) then the error is lower bounded by a constant. If we want error ≤ 1/2 then we need T ∈ Ω(N) queries. We apply this to show that a quantum computer cannot do much better than a classical computer...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
سال: 1999
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.1999.0397