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Justin Yirka (Mar 18 2024).

Abstract: We give a corrected proof that if PP $\subseteq$ BQP/qpoly, then the Counting Hierarchy collapses, as originally claimed by Aaronson CCC’06 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.

Arxiv: https://arxiv.org/abs/2403.09994