Achieve fully efficient verification for Hidden Code Sampling

Develop a fully efficient verification procedure for the Hidden Code Sampling approach to conditionally peaked quantum outputs, rather than relying on verification whose efficiency is only conditional on simulation-cost assumptions.

Background

The paper situates its obfuscation-based protocol in the broader context of peaked circuit sampling, where a hidden high-probability output is intended to serve as a certificate of quantum advantage. It contrasts its own polynomial-time public-verification result with Hidden Code Sampling, a related approach involving conditionally peaked outputs.

For Hidden Code Sampling, the cited work establishes that verification is cheaper than full simulation under assumptions on simulation cost, but does not establish fully efficient verification. The unresolved problem is therefore to obtain verification whose efficiency is unconditional within the relevant construction.