Relative to a particular quantum unitary oracle QMA is not contained in polyQCPH, although QMA is contained in polyQCPH for every classical oracle; the same separation is claimed for a distributional oracle.
The Power of a Single Haar Random State: Constructing and Separating Quantum Pseudorandomness
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Non-Standard Oracles for Bounded-Error Complexity Classes
Relative to a particular quantum unitary oracle QMA is not contained in polyQCPH, although QMA is contained in polyQCPH for every classical oracle; the same separation is claimed for a distributional oracle.