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