Under time evolution with a fixed Hamiltonian, a state 1-design of initial states grows into an approximate state k-design, with a proven recursion for GUE Hamiltonians and numerical evidence for a mixed-field Ising chain.
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State $k$-designs from Hamiltonian evolution
Under time evolution with a fixed Hamiltonian, a state 1-design of initial states grows into an approximate state k-design, with a proven recursion for GUE Hamiltonians and numerical evidence for a mixed-field Ising chain.