Quantum-Inspired Classical Algorithms for Singular Value Transformation
A recent breakthrough by Tang (STOC 2019) showed how to "dequantize" the quantum algorithm for recommendation systems by Kerenidis and Prakash (ITCS 2017). The resulting algorithm, classical but "quantum-inspired", efficiently computes a low-rank approximation of the users' preference matrix. Subsequent works have shown how to construct efficient quantum-inspired algorithms for approximating the pseudo-inverse of a low-rank matrix as well, which can be used to (approximately) solve low-rank linear systems of equations. In the present paper, we pursue this line of research and develop quantum-inspired algorithms for a large class of matrix transformations that are defined via the singular value decomposition of the matrix. In particular, we obtain classical algorithms with complexity polynomially related (in most parameters) to the complexity of the best quantum algorithms for singular value transformation recently developed by Chakraborty, Gilyén and Jeffery (ICALP 2019) and Gilyén, Su, Low and Wiebe (STOC 2019).
Sampling algorithms
quantum-inspired algorithms
linear algebra
Theory of computation~Design and analysis of algorithms
53:1-53:14
Regular Paper
A full version of the paper is available at https://arxiv.org/abs/1910.05699.
The authors are grateful to András Gilyén for discussions and comments about the manuscript. Part of this work has been done when DJ was visiting Kyoto University.
Dhawal
Jethwani
Dhawal Jethwani
Indian Institute of Technology (BHU), Varanasi, India
François
Le Gall
François Le Gall
Nagoya University, Japan
FLG was partially supported by JSPS KAKENHI grants Nos. JP15H01677, JP16H01705, JP16H05853, JP19H04066 and by the MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) grant No. JPMXS0118067394.
Sanjay K.
Singh
Sanjay K. Singh
Indian Institute of Technology (BHU), Varanasi, India
10.4230/LIPIcs.MFCS.2020.53
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Dhawal Jethwani, François Le Gall, and Sanjay K. Singh
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