A Note on the Quantum Query Complexity of Permutation Symmetric Functions

Chailloux, André

doi:10.4230/LIPIcs.ITCS.2019.19

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Theory of computation → Quantum query complexity

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quantum query complexity
permutation symmetric functions

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Abstract

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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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) https://doi.org/10.4230/LIPIcs.ITCS.2019.19

References

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A. Ambainis. Understanding Quantum Algorithms via Query Complexity. ArXiv e-prints, December 2017. URL: http://arxiv.org/abs/1712.06349.
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A Note on the Quantum Query Complexity of Permutation Symmetric Functions

Author André Chailloux

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