Classical and Quantum Polynomial Freiman-Ruzsa Algorithms

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

Published: 2026, Last Modified: 23 Mar 2026ITCS 2026EveryoneRevisionsBibTeXCC BY-SA 4.0
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.