QMA vs. QCMA and Pseudorandomness
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915093321613312 |
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| author | Liu, Jiahui Mutreja, Saachi Yuen, Henry |
| author_facet | Liu, Jiahui Mutreja, Saachi Yuen, Henry |
| contents | We study a longstanding question of Aaronson and Kuperberg on whether there exists a classical oracle separating $\mathsf{QMA}$ from $\mathsf{QCMA}$. Settling this question in either direction would yield insight into the power of quantum proofs over classical proofs. We show that such an oracle exists if a certain quantum pseudorandomness conjecture holds. Roughly speaking, the conjecture posits that quantum algorithms cannot, by making few queries, distinguish between the uniform distribution over permutations versus permutations drawn from so-called "dense" distributions.
Our result can be viewed as establishing a "win-win" scenario: either there is a classical oracle separation of $\mathsf{QMA}$ from $\mathsf{QCMA}$, or there is quantum advantage in distinguishing pseudorandom distributions on permutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | QMA vs. QCMA and Pseudorandomness Liu, Jiahui Mutreja, Saachi Yuen, Henry Quantum Physics Computational Complexity We study a longstanding question of Aaronson and Kuperberg on whether there exists a classical oracle separating $\mathsf{QMA}$ from $\mathsf{QCMA}$. Settling this question in either direction would yield insight into the power of quantum proofs over classical proofs. We show that such an oracle exists if a certain quantum pseudorandomness conjecture holds. Roughly speaking, the conjecture posits that quantum algorithms cannot, by making few queries, distinguish between the uniform distribution over permutations versus permutations drawn from so-called "dense" distributions. Our result can be viewed as establishing a "win-win" scenario: either there is a classical oracle separation of $\mathsf{QMA}$ from $\mathsf{QCMA}$, or there is quantum advantage in distinguishing pseudorandom distributions on permutations. |
| title | QMA vs. QCMA and Pseudorandomness |
| topic | Quantum Physics Computational Complexity |
| url | https://arxiv.org/abs/2411.14416 |