Concept classes satisfying quantum-learnability and classical-hardness criteria

Determine whether there exists a Boolean concept class that is not efficiently classically PAC learnable with respect to the uniform distribution and the PEX oracle, but is efficiently quantumly PAC learnable with respect to the uniform distribution and the PEX oracle.

Background

The proposed reverse implication would produce a separation between classical and quantum PAC GEN learning if one could identify a Boolean concept class that is hard for classical learners but efficiently learnable by quantum learners, with both learners receiving classical examples.

The paper notes that the existence of a concept class satisfying these two criteria was unresolved at the time of writing. Although the paper establishes a quantum-versus-classical example separation by a different oracle construction, it does not resolve this particular concept-class question.

References

Though it is currently not known whether a concept class does satisfy the above two criteria, proving the reverse direction of this conjecture true would allow one to instantly leverage such a concept class, if it exists, into a PAC GEN-learning separation.

— A Quantum/Classical Example Oracle Separation for Making Things Up  (2608.11648 - Chen, 12 Aug 2026) in Section 3.1, subsection “Context Of Prior Work by Sweke et al.”