A quantum algorithm to estimate the Gowers U2 norm and linearity testing of Boolean functions

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

Abstract: We propose a quantum algorithm to estimate the Gowers $$U_2$$ 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 $$\epsilon $$ 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 $$U_3$$ U 3 norms of Boolean functions.