State $k$-designs from Hamiltonian evolution

arXiv:2607.18537v1 Announce Type: new Abstract: We study the generation of state $k$-designs from time evolution under a fixed Hamiltonian. Specifically, we consider the ensemble $\mathcal{E}=\left\{e^{-iHt}|\psi_0\rangle | \ t\sim \mathrm{Unif}[0,T],\, |\psi_0\rangle\sim \mathcal{E}'\right\}$, whe