Which simulator observables have size-independent error bounds?
In plain words
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.
Precise statement
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.
What would settle it
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 in the literature
Unverified 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.