Tightness of ground-state heating as a predictor of stationary-state error

Determine whether a stationary-state error bound based on the ground-state heating rate of truncated jumps divided by the Lindbladian gap is tight in regimes where localized filtered-jump dynamics successfully prepares the ground state.

Background

The paper’s rigorous truncation theorem controls the perturbation using an induced generator norm, which is a worst-case quantity over all input states, together with a mixing estimate. Numerically, the authors also examine the ground-state heating diagnostic Γ↑(R*) and find that it tracks the observed outcomes for several chain models.

The authors identify a potentially sharper alternative: charge the truncation error only on the ground state and normalize it by the Lindbladian gap. They explicitly leave unresolved whether such a bound would be tight in cases where the localized-patch method works.

References

Whether a bound that charges the patch error only at the ground state, such as $\Gamma_\uparrow$ over the Lindbladian gap, would be tight where the method works is an empirical question that the global bound leaves open.

— Locality and filter design for dissipative ground-state preparation  (2609.31266 - Elman, 25 Sep 2026) in Section Discussion (Section 4), paragraph beginning “The chain experiments also show what the bound does not”