



01473nas a2200157   4500008004100000245008200041210006900123260001500192300001400207490000700221520099100228100001701219700002701236700001501263856003701278       2019                        eng d00aSublinear quantum algorithms for training linear and kernel-based classifiers0 aSublinear quantum algorithms for training linear and kernelbased  c04/03/2019  a3815-38240 v973 a<p>We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given n d-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training classifiers with constant margin runs in O~(n+d) time. We design sublinear quantum algorithms for the same task running in O~(n&minus;&minus;&radic;+d&minus;&minus;&radic;) time, a quadratic improvement in both n and d. Moreover, our algorithms use the standard quantization of the classical input and generate the same classical output, suggesting minimal overheads when used as subroutines for end-to-end applications. We also demonstrate a tight lower bound (up to poly-log factors) and discuss the possibility of implementation on near-term quantum machines. As a side result, we also give sublinear quantum algorithms for approximating the equilibria of n-dimensional matrix zero-sum games with optimal complexity Θ~(n&minus;&minus;&radic;).&nbsp;</p>1 aLi, Tongyang1 aChakrabarti, Shouvanik1 aWu, Xiaodi  uhttps://arxiv.org/abs/1904.02276