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Randomized and Quantum Approximate Matrix Multiplication

Authors Simon Apers , Arjan Cornelissen , Samson Wang

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LIPIcs.MFCS.2026.77.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Sketching and sampling
  • Theory of computation → Quantum computation theory
Keywords
  • randomized algorithms
  • quantum algorithms
  • streaming
  • approximate matrix multiplication
  • mean estimation

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Abstract

The complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution in faster time. In this work, we adopt a unifying perspective that frames these randomized algorithms in terms of mean estimation. Using it, we first give refined analyses of classical algorithms based on random walks by Cohen-Lewis (`99), and based on sketching by Sarlós (`06) and Drineas-Kannan-Mahoney (`06). We then propose an improvement on Cohen-Lewis that yields a single classical algorithm that is faster than all the other approaches, if we assume no use of (exact) fast matrix multiplication as a subroutine. Second, we demonstrate a quantum speedup on top of these algorithms by using the recent quantum multivariate mean estimation algorithm by Cornelissen-Hamoudi-Jerbi (`22).

Cite As Get BibTex

Simon Apers, Arjan Cornelissen, and Samson Wang. Randomized and Quantum Approximate Matrix Multiplication. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 77:1-77:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.MFCS.2026.77

Author Details

Simon Apers
  • Université Paris Cité, CNRS, IRIF, France
Arjan Cornelissen
  • Simons Institute, UC Berkeley, CA, USA
Samson Wang
  • Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA

References

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