Researchers at Princeton model a quantum world with limited complexity gains

Researchers at Princeton University and Kyoto University have demonstrated a scenario where evidence of quantum advantage can coexist with the theoretical equivalence of P and NP. The work details a classical oracle, a hypothetical computational tool, relative to which both proofs of quantumness and the equality of P^O and NP^O hold true, challenging a common assumption that quantum advantage necessarily implies P ≠ NP. The researchers also constructed an oracle where BQPO equals PSPACEO, indicating a significant leap in classical computational power. These oracle separations have direct implications for cryptography; the findings suggest proofs of quantumness cannot reliably construct classical or quantum cryptography, and quantum oblivious transfer cannot build post-quantum one-way functions, under specific conditions. A newly constructed classical oracle demonstrates a scenario where proofs of quantumness can exist even if P equals NP, a result challenging conventional assumptions about the relationship between quantum advantage and computational complexity. The finding suggests that demonstrating quantum capabilities does not automatically preclude…