Instantiate the membership oracle under computational assumptions

Construct an explicit, non-oracular instantiation of the balanced folded OPI membership oracles that yields a quantum advantage comparable to the oracle-based result, conditionally on computational complexity assumptions.

Background

The balanced folded OPI separation relies on acceptance sets that are accessed through membership oracles. Although the folded Reed–Solomon code, evaluation points, and algebraic structure are explicit, the acceptance sets themselves are oracle-defined, and the oracle prevents classical algorithms from exploiting additional structure in those sets.

The discussion identifies replacing this oracle by an explicit computational construction as an open direction. The intended goal is a similar quantum-versus-classical separation whose validity is based on computational complexity assumptions rather than an abstract oracle.