Depth-efficient proofs of quantumness

A proof of quantumness is a type challenge-response protocol in which classical verifier can efficiently certify the quantum advantage an untrusted prover. That is, quantum prover correctly answer verifier's challenges and be accepted, while any polynomial-time will rejected with high probability, based on plausible computational assumptions. To challenges, existing proofs typically require to perform combination polynomial-size circuits measurements. In this paper, we give two constructions need only mathvariant="italic">constant-depth circuits (and measurements) together log-depth computation. Our first construction generic compiler that allows us translate all into constant depth versions. second around mathvariant="italic">learning rounding problem, yields shorter requiring fewer qubits than construction. addition, also has some robustness against noise.