Efficient quantum algorithms for (Gapped) group testing and junta testing

Andris Ambainis, Aleksandrs Belovs, Oded Regev, Ronald De Wolf

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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(k1/3) queries for junta-testing (for constant ∈).

Original languageEnglish (US)
Title of host publication27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
EditorsRobert Krauthgamer
PublisherAssociation for Computing Machinery
Pages903-922
Number of pages20
ISBN (Electronic)9781510819672
StatePublished - Jan 1 2016
Event27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 - Arlington, United States
Duration: Jan 10 2016Jan 12 2016

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume2

Other

Other27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
CountryUnited States
CityArlington
Period1/10/161/12/16

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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  • Cite this

    Ambainis, A., Belovs, A., Regev, O., & De Wolf, R. (2016). Efficient quantum algorithms for (Gapped) group testing and junta testing. In R. Krauthgamer (Ed.), 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.