Quantum-Inspired Classical Algorithms for Singular Value Transformation

Authors Dhawal Jethwani, François Le Gall, Sanjay K. Singh

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Dhawal Jethwani
  • Indian Institute of Technology (BHU), Varanasi, India
François Le Gall
  • Nagoya University, Japan
Sanjay K. Singh
  • Indian Institute of Technology (BHU), Varanasi, India


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.

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Dhawal Jethwani, François Le Gall, and Sanjay K. Singh. Quantum-Inspired Classical Algorithms for Singular Value Transformation. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 53:1-53:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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).

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Sampling algorithms
  • quantum-inspired algorithms
  • linear algebra


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