Even quantum advice is unlikely to solve PP

Justin Yirka

doi:10.4086/toc.2025.v021a007

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arXiv · 2403.09994

Even quantum advice is unlikely to solve PP

Justin Yirka

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Abstract

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.

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BibTeX RIS

Justin Yirka. 2024-03-15. Even quantum advice is unlikely to solve PP. https://doi.org/10.4086/toc.2025.v021a007

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