188网体育

【基础沙龙】第36期-王春昊


主讲人188网体育: 王春昊,博士,德州大学奥斯汀分校计算机系博士后研究员

主题188网体育: Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning

时间188网体育: 2020年1月14日星期二,10:00-11:00

地点188网体育: 沙河校区通信楼725室

主讲人简介:

WANGCHUNHAO,BOSHI,XIANDEZHOUDAXUEAOSITINGFENXIAOJISUANJIXIBOSHIHOUYANJIUYUAN。2009NIANBENKEBIYEYUZHEJIANGDAXUEJISUANJIXI,2011NIANSHUOSHIBIYEYUJIANADAXIMENFULEIZEDAXUEJISUANJIXI,2018NIANBOSHIBIYEYUJIANADAHUATIELUDAXUEJISUANJIXI。WANGCHUNHAOBOSHIZHANGQICONGSHIJISUANJISUANFAYIJILIANGZIJISUANLILUNYANJIU,MUQIANZHILIYULIANGZIMONI,LIANGZIJIQIXUEXI,LIANGZIYOUHUASUANFA,LIANGZIJISUANFUZADUDENGFANGMIANDEYANJIU,XIANYIYOUDUOPIANLUNWENBEILILUNLIANGZIJISUANDINGJIHUIYIQIPJIESHOU。

报告摘要:

We present an algorithmic framework generalizing quantum-inspired polylogarithmic-time algorithms on low-rank matrices. Our work follows the line of research started by Tang's breakthrough classical algorithm for recommendation systems [STOC'19]. The main result of this work is an algorithm for singular value transformation on low-rank inputs in the quantum-inspired regime, where singular value transformation is a framework proposed by Gilyén et al. [STOC'19] to study various quantum speedups. Since singular value transformation encompasses a vast range of matrix arithmetic, this result, combined with simple sampling lemmas from previous work, suffices to generalize all results dequantizing quantum machine learning algorithms to the authors' knowledge. Via simple black-box applications of our singular value transformation framework, we recover the dequantization results on recommendation systems, principal component analysis, supervised clustering, low-rank matrix inversion, low-rank semidefinite programming, and support vector machines. We also give additional dequantizations results on low-rank Hamiltonian simulation and discriminant analysis.

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