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Classical and Quantum Polynomial Freiman-Ruzsa Algorithms

Authors Srinivasan Arunachalam , Davi Castro-Silva , Arkopal Dutt , Tom Gur

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ACM Subject Classification
  • Theory of computation → Randomness, geometry and discrete structures
Keywords
  • Additive combinatorics
  • sublinear algorithms

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Abstract

We prove algorithmic versions of the polynomial Freiman-Ruzsa theorem of Gowers, Green, Manners, and Tao (Annals of Mathematics, 2025) in additive combinatorics. In particular, we give classical and quantum polynomial-time algorithms that, for A ⊆ 𝔽₂ⁿ with doubling constant K, learn an explicit description of a subspace V ⊆ 𝔽₂ⁿ of size |V| ≤ |A| such that A can be covered by K^C translates of V, for a universal constant C > 1.

Cite As Get BibTex

Srinivasan Arunachalam, Davi Castro-Silva, Arkopal Dutt, and Tom Gur. Classical and Quantum Polynomial Freiman-Ruzsa Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 11:1-11:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.11

Author Details

Srinivasan Arunachalam
  • IBM Quantum, Almaden Research Center, Almaden, CA, USA
Davi Castro-Silva
  • Department of Computer Science and Technology, University of Cambridge, UK
Arkopal Dutt
  • IBM Quantum, Cambridge, MA, USA
Tom Gur
  • Department of Computer Science and Technology, University of Cambridge, UK

Funding

  • Castro-Silva, Davi: Supported by ESPRC Robust and Reliable Quantum Computing Grant.
  • Gur, Tom: Supported by ERC Starting Grant 101163189 and UKRI Future Leaders Fellowship MR/X023583/1.

Acknowledgements

We want to thank Jop Briët for multiple discussions. We also want to thank the anonymous ITCS and QIP reviewers who helped improve an earlier version of the paper.

References

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