Establish the system-size scaling of the Lindblad step size

Determine whether the Lindblad step size required to achieve a fixed target accuracy per unit of simulation time remains constant as the system size increases for the empirical parameter regimes of the single-ancilla Lindblad ground-state preparation algorithm.

Background

The paper infers empirical step-size parameters from small one-dimensional Hubbard chains and assumes that the step size needed for one unit of evolution is independent of system size. This assumption directly affects the extrapolated fault-tolerant resource estimates for larger systems.

The available simulations provide only indicative evidence because they involve small lattices. If the required step size decreases with system size, the reported costs for classically nontrivial systems would be underestimates. Determining the asymptotic behavior of this parameter is therefore unresolved.

References

However, such small systems can only be indicative of the larger lattices that we aim to cost, so it is possible that the step size required for a single time unit does not stay constant with system size, so in this sense our estimates are more of a lower bound to the actual cost.

— Fault-tolerant resource estimation for ground-state preparation via Lindblad simulation  (2610.08667 - Bothe et al., 6 Oct 2026) in Appendix, Section 10, Empirical spectral properties and time steps