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. 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 separation of QMA and QCMA relative to a distributional quantumly-accessible classical oracles, which was recently shown by Natarajan and Nirkhe.

翻译：构造一个相对于BQP/qpoly $\neq$ BQP/poly或QMA $\neq$ QCMA的经典谕示是一个长期悬而未决的问题。本文构造了经典可访问的经典谕示，使得BQP/qpoly $\neq$ BQP/poly。此处，经典可访问的经典谕示指即使对于量子算法也只能以经典方式访问的谕示。基于类似技术，我们还给出了一个关于分布性量子可访问经典谕示下QMA与QCMA分离的替代证明，该结果由Natarajan和Nirkhe近期提出。