English

A quantum algorithm to estimate the Gowers $U_2$ norm and linearity testing of Boolean functions

Discrete Mathematics 2020-07-01 v1 Quantum Physics

Abstract

We propose a quantum algorithm to estimate the Gowers U2U_2 norm of a Boolean function, and extend it into a second algorithm to distinguish between linear Boolean functions and Boolean functions that are ϵ\epsilon-far from the set of linear Boolean functions, which seems to perform better than the classical BLR algorithm. Finally, we outline an algorithm to estimate Gowers U3U_3 norms of Boolean functions.

Keywords

Cite

@article{arxiv.2006.16523,
  title  = {A quantum algorithm to estimate the Gowers $U_2$ norm and linearity testing of Boolean functions},
  author = {C. A. Jothishwaran and Anton Tkachenko and Sugata Gangopadhyay and Constanza Riera and Pantelimon Stanica},
  journal= {arXiv preprint arXiv:2006.16523},
  year   = {2020}
}
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