Sampling-Based Sublinear Low-Rank Matrix Arithmetic Framework for Dequantizing Quantum Machine Learning Nai-Hui Chia András Gilyén Tongyang Li University of Texas at Austin California Institute of Technology University of Maryland Austin, Texas, USA Pasadena, California, USA College Park, Maryland, USA
[email protected] [email protected] [email protected] Han-Hsuan Lin Ewin Tang Chunhao Wang University of Texas at Austin University of Washington University of Texas at Austin Austin, Texas, USA Seattle, Washington, USA Austin, Texas, USA
[email protected] [email protected] [email protected] ABSTRACT KEYWORDS We present an algorithmic framework for quantum-inspired clas- quantum machine learning, low-rank approximation, sampling, sical algorithms on close-to-low-rank matrices, generalizing the quantum-inspired algorithms, quantum machine learning, dequan- series of results started by Tang’s breakthrough quantum-inspired tization algorithm for recommendation systems [STOC’19]. Motivated by ACM Reference Format: quantum linear algebra algorithms and the quantum singular value Nai-Hui Chia, András Gilyén, Tongyang Li, Han-Hsuan Lin, Ewin Tang, transformation (SVT) framework of Gilyén et al. [STOC’19], we and Chunhao Wang. 2020. Sampling-Based Sublinear Low-Rank Matrix develop classical algorithms for SVT that run in time independent Arithmetic Framework for Dequantizing Quantum Machine Learning. In of input dimension, under suitable quantum-inspired sampling Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Com- assumptions. Our results give compelling evidence that in the cor- puting (STOC ’20), June 22–26, 2020, Chicago, IL, USA. ACM, New York, NY, responding QRAM data structure input model, quantum SVT does USA, 14 pages.