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arXiv · 2609.07060

2-Fold Forrelation is in QAC$^0$

Francisca Vasconcelos
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Abstract

We show that 2-fold Forrelation with inverse-polylogarithmic promise gap can be solved, with bounded error, by polynomial-size QAC$^0$ circuits. Unlike the standard oracle-based Forrelation algorithm, our circuits receive the input explicitly, in the same form as the AC$^0$ circuits against which Forrelation is known to be hard. At constant gap, this yields a natural promise-problem separation between QAC$^0$ and AC$^0$.

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Francisca Vasconcelos. 2026-09-07. 2-Fold Forrelation is in QAC$^0$. https://arxiv.org/abs/2609.07060

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