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2-Fold Forrelation is in QAC$^0$

Year: 2026

Type: preprint

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$^0$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.07060

Author: Vasconcelos, Francisca

Institution: University of California, Berkeley

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy

Awards: G111448035, G5662364344, G7456145480, FET: Medium: Quantum Algorithms, Complexity, Testing and Benchmarking

OpenAlex ID: W7212045030

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