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Conference Papers Year : 2019

## A note on the quantum query complexity of permutation symmetric functions

André Chailloux

#### Abstract

It is known since the work of [AA14] 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 $R(f) = \widetilde{O}\left(Q^7(f)\right)$. In this paper, we improve this result and show that $R(f) = {O}\left(Q^3(f)\right)$ 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 [Zha15].

### Dates and versions

hal-01950650 , version 1 (11-12-2018)

### Identifiers

• HAL Id : hal-01950650 , version 1
• ARXIV :
• DOI :

### Cite

André Chailloux. A note on the quantum query complexity of permutation symmetric functions. ITCS 2019 - 10th Annual Innovations in Theoretical Computer Science, Jan 2019, San Diego, United States. ⟨10.4230/LIPIcs.ITCS.2019.19⟩. ⟨hal-01950650⟩

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