Exact Quantum Query Complexity of EXACT and THRESHOLD

Authors Andris Ambainis, Janis Iraids, Juris Smotrovs

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Andris Ambainis
Janis Iraids
Juris Smotrovs

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Andris Ambainis, Janis Iraids, and Juris Smotrovs. Exact Quantum Query Complexity of EXACT and THRESHOLD. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 263-269, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


A quantum algorithm is exact if it always produces the correct answer, on any input. Coming up with exact quantum algorithms that substantially outperform the best classical algorithm has been a quite challenging task. In this paper, we present two new exact quantum algorithms for natural problems: - for the problem EXACT_k^n in which we have to determine whether the sequence of input bits x_1, ..., x_n contains exactly k values x_i=1; - for the problem THRESHOLD_k^n in which we have to determine if at least k of n input bits are equal to 1.
  • Quantum query algorithms
  • Complexity of Boolean functions


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