Even quantum advice is unlikely to solve PP
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918216673001472 |
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| author | Yirka, Justin |
| author_facet | Yirka, Justin |
| contents | We give a corrected proof that if PP $\subseteq$ BQP/qpoly, then the Counting Hierarchy collapses, as originally claimed by [Aaronson 2006 arXiv:cs/0504048]. This recovers the related unconditional claim that PP does not have circuits of any fixed size $n^k$ even with quantum advice. We do so by proving that YQP*, an oblivious version of (QMA $\cap$ coQMA), is contained in APP, and so is PP-low. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09994 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Even quantum advice is unlikely to solve PP Yirka, Justin Computational Complexity Quantum Physics We give a corrected proof that if PP $\subseteq$ BQP/qpoly, then the Counting Hierarchy collapses, as originally claimed by [Aaronson 2006 arXiv:cs/0504048]. This recovers the related unconditional claim that PP does not have circuits of any fixed size $n^k$ even with quantum advice. We do so by proving that YQP*, an oblivious version of (QMA $\cap$ coQMA), is contained in APP, and so is PP-low. |
| title | Even quantum advice is unlikely to solve PP |
| topic | Computational Complexity Quantum Physics |
| url | https://arxiv.org/abs/2403.09994 |