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A quantum algorithm to estimate the Gowers $U_2$ norm and linearity testing of Boolean functions
arXiv - CS - Discrete Mathematics Pub Date : 2020-06-30 , DOI: arxiv-2006.16523 C. A. Jothishwaran, Anton Tkachenko, Sugata Gangopadhyay, Constanza Riera, Pantelimon Stanica
arXiv - CS - Discrete Mathematics Pub Date : 2020-06-30 , DOI: arxiv-2006.16523 C. A. Jothishwaran, Anton Tkachenko, Sugata Gangopadhyay, Constanza Riera, Pantelimon Stanica
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.
中文翻译:
估计布尔函数的 Gowers $U_2$ 范数和线性测试的量子算法
我们提出了一种量子算法来估计布尔函数的 Gowers $U_2$ 范数,并将其扩展为第二种算法,以区分线性布尔函数和远离线性布尔函数集的布尔函数,这似乎比经典的 BLR 算法性能更好。最后,我们概述了一种估计布尔函数的 Gowers $U_3$ 范数的算法。
更新日期:2020-07-01
中文翻译:
估计布尔函数的 Gowers $U_2$ 范数和线性测试的量子算法
我们提出了一种量子算法来估计布尔函数的 Gowers $U_2$ 范数,并将其扩展为第二种算法,以区分线性布尔函数和远离线性布尔函数集的布尔函数,这似乎比经典的 BLR 算法性能更好。最后,我们概述了一种估计布尔函数的 Gowers $U_3$ 范数的算法。