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arXiv · 2006.16523

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

C. A. Jothishwaran·Anton Tkachenko·Sugata Gangopadhyay·Constanza Riera·Pantelimon Stanica
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Abstract

We propose a quantum algorithm to estimate the Gowers $U_2$ norm of a Boolean function, and extend it into a second algorithm to distinguish between linear Boolean functions and Boolean functions that are $\epsilon$-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 $U_3$ norms of Boolean functions.

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C. A. Jothishwaran, Anton Tkachenko, Sugata Gangopadhyay, Constanza Riera, Pantelimon Stanica. 2020-06-30. A quantum algorithm to estimate the Gowers $U_2$ norm and linearity testing of Boolean functions. https://arxiv.org/abs/2006.16523

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