Journal ArticleSublinear quantum algorithms for training linear and kernel-based classifiersLi, Tongyang; Chakrabarti, Shouvanik; Wu, XiaodiWe 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 by Clarkson et al. runs in Õ (n+d), which is also optimal in its input/output model. We design sublinear quantum algorithms for the same task running in Õ (\sqrt{n}+\sqrt{d}), 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.2019-06-0110106372Proceedings of Machine Learning Research973815-38242640-3498https://doi.org/1816695National Science Foundation