A constant-time, translation-invariant Hamiltonian quantum simulation architecture is proven to form an approximate unitary 2-design, implying anticoncentration, and its output probabilities are proven #P-hard to compute on average.
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Closing gaps of a quantum advantage with short-time Hamiltonian dynamics
A constant-time, translation-invariant Hamiltonian quantum simulation architecture is proven to form an approximate unitary 2-design, implying anticoncentration, and its output probabilities are proven #P-hard to compute on average.