State $k$-designs from Hamiltonian evolution

Shengxian Hou, Zong-Yue Hou, Zhi-Cheng Yang

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}|ψ_0\rangle | \ t\si…