2-Fold Forrelation is in QAC$^0$

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$^0$.

Quantum Physics (quant-ph); Computational Complexity (cs.CC)

arXiv:2609.07060 [quant-ph]

(or arXiv:2609.07060v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.07060 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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