### Abstract

In the k-junta testing problem, a tester has to efficiently decide whether a given function f: {0,1}^{n} → {0,1} is a k-junta (i.e., depends on at most k of its input bits) or is ∈-far from any k-junta. Our main result is a quantum algorithm for this problem with query complexity Ō(√∈) and time complexity Ō(n√∈). This quadratically improves over the query complexity of the previous best quantum junta tester, due to Atici and Servedio. Our tester is based on a new quantum algorithm for a gapped version of the combinatorial group testing problem, with an up to quartic improvement over the query complexity of the best classical algorithm. For our upper bound on the time complexity we give a near-linear time implementation of a shallow variant of the quantum Fourier transform over the symmetric group, similar to the Schur-Weyl transform. We also prove a lower bound of ω(k^{1/3}) queries for junta-testing (for constant ∈).

Original language | English (US) |
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Title of host publication | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 |

Editors | Robert Krauthgamer |

Publisher | Association for Computing Machinery |

Pages | 903-922 |

Number of pages | 20 |

ISBN (Electronic) | 9781510819672 |

State | Published - 2016 |

Event | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 - Arlington, United States Duration: Jan 10 2016 → Jan 12 2016 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | 2 |

### Other

Other | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 |
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Country | United States |

City | Arlington |

Period | 1/10/16 → 1/12/16 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

*27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016*(pp. 903-922). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2). Association for Computing Machinery.