Classically verifiable quantum advantage on pre-fault-tolerant hardware
In plain words
Current advantage experiments produce outputs that a classical computer cannot check without redoing the hard calculation. A task that today's noisy machines can perform, that is hard classically, and whose answer is quick to check has not been demonstrated.
Precise statement
Find a task executable by circuits of depth $O(\operatorname{polylog} n)$ on $n \le 10^{3}$ qubits with two-qubit gate error $\sim 10^{-3}$ and no error correction such that (i) a classical verifier checks the output in $\operatorname{poly}(n)$ time, (ii) the task is classically hard under a standard assumption such as learning with errors, and (iii) soundness holds at the output fidelity actually achievable. Answer: a protocol with all three properties, or a no-go result relating verifiability, noise rate and depth.
What would settle it
An experiment executing such a protocol at a size where the classical cost is established, or a theorem excluding it.
Status in the literature
Unverified note
Many 2025-2026 proposals (low-depth lattice-based, planted-structure and obfuscation-based schemes, e.g. arXiv:2609.01448, arXiv:2609.39918) address subsets of these conditions.