The power of quantum circuits in sampling
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912629413380096 |
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| author | Blanc, Guy Koch, Caleb Lange, Jane Strassle, Carmen Tan, Li-Yang |
| author_facet | Blanc, Guy Koch, Caleb Lange, Jane Strassle, Carmen Tan, Li-Yang |
| contents | 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 $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The power of quantum circuits in sampling Blanc, Guy Koch, Caleb Lange, Jane Strassle, Carmen Tan, Li-Yang Quantum Physics Computational Complexity 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 $k$. |
| title | The power of quantum circuits in sampling |
| topic | Quantum Physics Computational Complexity |
| url | https://arxiv.org/abs/2510.03645 |