On the Complexity of Searching for a Maximum of a Function on a Quantum Computer |
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Authors: | Maciej Go?win |
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Affiliation: | (1) Department of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, paw. B7, II p., pok. 24, 30-059 Cracow, Poland |
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Abstract: | We deal with the problem of finding a maximum of a function from the Hölder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses a pre-existing quantum algorithm for finding maximum of a discrete sequence. To prove lower bounds we use results for finding the logical OR of sequence of bits. We show that quantum computation yields a quadratic speed-up over deterministic and randomized algorithms. |
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Keywords: | Numerical optimization optimal algorithm quantum computing query complexity |
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