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On the Complexity of Searching for a Maximum of a Function on a Quantum Computer

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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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This research was partly supported by AGH grant no. 10.420.03

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  1. Department of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, paw. B7, II p., pok. 24, 30-059, Cracow, Poland

    Maciej Goćwin

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  1. Maciej Goćwin
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Goćwin, M. On the Complexity of Searching for a Maximum of a Function on a Quantum Computer. Quantum Inf Process 5, 31–41 (2006). https://doi.org/10.1007/s11128-006-0011-8

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