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.

翻译：我们给出了修正后的证明：如果PP $\subseteq$ BQP/qpoly，那么计数层次将坍缩，这一结论最初由Aaronson在CCC'06 arXiv:cs/0504048中声称。这恢复了相关的无条件断言：即使有量子建议，PP也不具有任何固定规模$n^k$的电路。我们通过证明YQP*（一种(QMA $\cap$ coQMA)的遗忘版本）包含于APP，从而属于PP-low类来实现这一点。