2-Fold Forrelation is in QAC0
Francisca Vasconcelos
Abstract
We show that 2-fold Forrelation with inverse-polylogarithmic promise gap can be solved, with bounded error, by polynomial-size QAC0 circuits. Unlike the standard oracle-based Forrelation algorithm, our circuits receive the input explicitly, in the same form as the AC0 circuits against which Forrelation is known to be hard. At constant gap, this yields a natural promise-problem separation between QAC0 and AC0.
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