{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"667c7c406f49ad76efa603e98860be8971562bdb17c042922335b53b345a0c02","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"80bc934749f9c584d209ffe662f8aa31f1727a42042392bafba1d5bc8ae48470","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"qi.useful-advantage.verifiable-advantage-noisy","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"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.","posed_since":"","precise":"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.","problem_ref":null,"references":"","settled_by":"An experiment executing such a protocol at a size where the classical cost is established, or a theorem excluding it.","status_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.","title":"Classically verifiable quantum advantage on pre-fault-tolerant 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