It is a long-standing open question to construct a classical oracle relative to which BQP/qpoly $\neq$ BQP/poly or QMA $\neq$ QCMA. In this paper, we construct classically-accessible classical oracles relative to which BQP/qpoly $\neq$ BQP/poly and QMA $\neq$ QCMA. Here, classically-accessible classical oracles are oracles that can be accessed only classically even for quantum algorithms. Based on a similar technique, we also show an alternative proof for the separation of QMA and QCMA relative to a distributional quantumly-accessible classical oracle, which was recently shown by Natarajan and Nirkhe.

翻译：本文旨在构造一个相对于某个经典预言机，对于BQP/qpoly ≠ BQP/poly和QMA ≠ QCMA，此预言机仅供经典 访问，这是一个长期未解决的问题。这里，“经典可访问的经典预言机”是指在量子算法下仅能经典访问的预言机。基于类似的技术，我们还展示了一个相对于分布式量子可访问的经典预言机的替代QCMA和QMA之间的分离证明，这是由Natarajan和Nirkhe最近证明的。