{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5589bbcf30fe66888446f6a37dd85784e61a3e985826110cfb72580c5847ba99","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["56759f0e87d83925e34bea2a27fec27d06150376ca877dbc81eb4c5764b3e5db","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"e94b9e0b9f6d234d53434ec61dee1d2867c0edea26ba873352613478be804e98","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":["ai:gpt-5.5"],"external_id":"amo.simulator-verification.error-stable-observables","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"Small errors in the controls might add up across many atoms and ruin a big simulation. The question is which measured quantities stay accurate no matter how big the system grows.","posed_since":"","precise":"Local Hamiltonian $H$ on $N$ sites; the device implements $H+\\sum_i \\delta h_i$ with $\\mid\\mid \\delta h_i\\mid\\mid \\le \\epsilon$. Characterize the classes of states (Gibbs states at temperature T, quench dynamics to time t) and local observables O for which $\\left|\\langle O\\rangle_{\\mathrm{device}}-\\langle O\\rangle_{\\mathrm{ideal}}\\right|\\le f(\\epsilon,T,t)$ independent of $N$. Answer: theorems with explicit $f$, and counterexamples outside these classes.","problem_ref":"56759f0e87d83925e34bea2a27fec27d06150376ca877dbc81eb4c5764b3e5db","references":"","settled_by":"Proofs of size-independent bounds for broad classes (for example all gapped ground states or Gibbs states above a threshold temperature) and explicit counterexamples elsewhere.","status_note":"2024 work proved such bounds for some Gibbs states and short-time dynamics (Trivedi, Franco Rubio, Cirac, Nature Communications); ground states and long-time dynamics remain open.","title":"Which simulator observables have size-independent error 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