The power of quantum circuits in sampling

• URL: http://arxiv.org/abs/2510.03645v1
• Date: Sat, 04 Oct 2025 03:19:47 GMT
• Title: The power of quantum circuits in sampling
• Authors: Guy Blanc, Caleb Koch, Jane Lange, Carmen Strassle, Li-Yang Tan,
• Abstract summary: We show, relative to a random oracle, that quantum-size circuits can sample distributions that subexponential-size classical circuits cannot approximate.<n>A key ingredient in our proof is a new hardness amplification lemma for the classical query complexity of the Yamakawa-Zhandry (2022) search problem.
• Score: 10.233615909288188
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We give new evidence that quantum circuits are substantially more powerful than classical circuits. We show, relative to a random oracle, that polynomial-size quantum circuits can sample distributions that subexponential-size classical circuits cannot approximate even to TV distance $1-o(1)$. Prior work of Aaronson and Arkhipov (2011) showed such a separation for the case of exact sampling (i.e. TV distance $0$), but separations for approximate sampling were only known for uniform algorithms. A key ingredient in our proof is a new hardness amplification lemma for the classical query complexity of the Yamakawa-Zhandry (2022) search problem. We show that the probability that any family of query algorithms collectively finds $k$ distinct solutions decays exponentially in $k$.

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