Classical vs Quantum Advice and Proofs Under Classically-Accessible Oracle
Xingjian Li, Liu, Qipeng, Angelos Pelecanos, Takashi Yamakawa · arXiv (Cornell University) · 2023
It is a long-standing open question to construct a classical oracle relative to which BQP/qpoly $ eq$ BQP/poly or QMA $ eq$ QCMA. In this paper, we construct classically-accessible classical oracles relative to which BQP/qpoly $ eq$ BQP/poly and QMA $ eq$ 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.