A Note on the Quantum Query Complexity of Permutation Symmetric Functions

Author André Chailloux

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André Chailloux
  • Inria de Paris, EPI SECRET, Paris, France

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André Chailloux. A Note on the Quantum Query Complexity of Permutation Symmetric Functions. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 19:1-19:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


It is known since the work of [Aaronson and Ambainis, 2014] that for any permutation symmetric function f, the quantum query complexity is at most polynomially smaller than the classical randomized query complexity, more precisely that R(f) = O~(Q^7(f)). In this paper, we improve this result and show that R(f) = O(Q^3(f)) for a more general class of symmetric functions. Our proof is constructive and relies largely on the quantum hardness of distinguishing a random permutation from a random function with small range from Zhandry [Zhandry, 2015].

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ACM Subject Classification
  • Theory of computation → Quantum query complexity
  • quantum query complexity
  • permutation symmetric functions


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