{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"3d97e1750913b1bfabb802bb615a0993525b91dda12f0ff326f544c7f42443cd","created":"2026-10-03T07:17:54Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"c6b4e35b327cdcedd8a061754ba9449c3a98c1e9c12b2bcd28a810536b37c426","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"amo.simulator-verification.error-stable-observables","kind":"well-posed","literature_status":"partially-resolved","n":"1","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 ||delta h_i|| <= 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":null,"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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