Fastest Quantum Search for Extreme Point
نویسنده
چکیده
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 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 quantum search for solution of equations f(x) = 1 where f is a Boolean function with b such solutions chosen at random with asymptotic probability 1 (n −→ ∞).
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