It is a long-standing open question to construct a classical oracle relative to which BQP/qpoly = BQP/poly or QMA = QCMA. In this paper, we construct classically-accessible classical oracles relative to which BQP/qpoly = BQP/poly and QMA = 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.

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