Asymptotic resource scaling of nucleation

Establish the asymptotic scaling of the total computational cost of the nucleation state-preparation algorithm with system size.

Background

The paper derives rigorous worst-case bounds on the total adiabatic evolution time and the number of first-order Trotter steps required at each nucleation stage. However, the numerical experiments indicate that these general bounds can substantially overestimate the resources required in practice. Because the algorithm consists of multiple local growth stages, the authors leave unresolved how the total cost accumulates as the lattice or system size increases.